Research Article Balanced Cluster Head Selection Based on …downloads.hindawi.com/journals/ijdsn/2016/5040475.pdf · 2016-03-10 · Research Article Balanced Cluster Head Selection

Research ArticleBalanced Cluster Head Selection Based on Modified k-Means ina Distributed Wireless Sensor Network

Sasikumar Periyasamy Sibaram Khara and Shankar Thangavelu

SENSE VIT University Vellore Tamil Nadu 632 014 India

Correspondence should be addressed to Sasikumar Periyasamy sasikumarpvitacin

Received 29 October 2015 Revised 2 February 2016 Accepted 11 February 2016

Academic Editor Antonio Lazaro

Copyright copy 2016 Sasikumar Periyasamy et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

A major problem with Wireless Sensor Networks (WSNs) is the maximization of effective network lifetime through minimizationof energy usage in the network nodes A modified k-means (Mk-means) algorithm for clustering was proposed which includesthree cluster heads (simultaneously chosen) for each cluster These cluster heads (CHs) use a load sharing mechanism to rotate asthe active cluster head which conserves residual energy of the nodes thereby extending network lifetime Moreover it reduces thenumber of times reclustering has to be done and significantly increases the number of data packets sent during network operationThe results show thatMk-means (modified k-means) algorithm was found to outperform the existing clustering algorithms owingto its unique multiple cluster head methodology

1 Introduction

Distributedwirelessmicrosensor networks have become veryimportant components in the day-to-day world of data com-putingMiniature in size is the key factor for designingmicro-sensors The battery in the sensor node is a major constraintof the miniaturization process It can only be reduced to aparticular degree due to energy density In addition to theimprovements to the energy density factor consumption ofenergy can also be reduced in sensorsThis approach requiresthe implementation and usage of low power hardware Alsothe operational lifetime of sensor nodes can be extendedby optimizing applications operating systems and protocolsused for communication In certain scenarios the on-boardcomponents were switched off when they are not sensing ortransmitting data That is they are idle

Categorizing sensor nodes to groups (by forming clusters)has become common among researchers in recent yearsThis clustering approach led to the development of morenumber of clustering algorithms Clustering guides the nodesto organize themselves intomultiple clusters with one sensornode acting as the CH And the rest of the noncluster headnodes transmit sensed information to their respective CHs

while the CHs aggregate the collected information and sendit to the distant BS

The current scheme of clustering addresses the self-organization and scalability properties with rotational basedCH selection Thereby a group is led by master (CH) nodewith energy conservation paradigm to send the data toBase Station (BS) We propose here the modified k-meansalgorithm with more than one CH in a cluster to leadthe group The sensor nodes in the cluster will chooseone of the CHs to send the data either distance based orschedule based So that the time and energy spent duringthe reclustering phase are reduced by decreasing the numberof reclustering rounds Further various applications demandextremely efficient support for top-k queries in getting datafrom WSN Hence adding the above processing graduallyreduces the data traffic when data forwarding happens onqueryrequirement based to the BS

The rest of the paper is organized as follows Detailedliterature survey on selected clustering algorithm is presentedin Section 2 followed by k-means clustering algorithm andMk-means clustering algorithms in Sections 3 and 4 respec-tively In Section 5 the performance is analyzed comparingthe algorithm proposed through simulations Finally conclu-sions are presented in Section 6

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2016 Article ID 5040475 11 pageshttpdxdoiorg10115520165040475

2 International Journal of Distributed Sensor Networks

2 Literature Survey

The last few years have witnessed a rapid increase inthe interest in the usage of WSN in various applicationslike disaster management habitat monitoring and militarysurveillance The sensor nodes in these environments weredeployed randomly and expected to operate independentlyin unsupervised area In this larger number of sensor nodesscalability is addressed by generally grouping the sensornodes intomultiple nonoverlapping clusters In [1] a detailedtaxonomy and generalized classification of various clusteringschemes were presented

The clustering process aims to extend the lifespan ofsensor nodes [2ndash5] Thereby by increasing the lifetime of theCH onewill be able tominimize the need for reclustering andless number of overheads exchanged between a microsensornode and CH The real challenge considered in the field ofclustering algorithms is how to influence the longevity ofsensor nodes in aWSN through comparison of initial energywith the residual energy of the node during each cycle orroundof communication [3] To simplify the depleted batterycauses the sensor nodes to fail soon

Linked Cluster Algorithm (LCA) Baker and Ephremides [6 7]are the first authors to consider clustering in WSN Theyfocused on creating an efficient topology of network thathad the capability to handle the mobility of the nodes Byperforming network clustering [1] the CHs are expected toform a backbone network to which cluster members canconnect while on the move The objective of the proposeddistributed algorithm is to form many clusters such that aCH is independently connected to all the sensor nodes in itsown cluster LCA is thus designed to maximize connectivityof the network But this algorithm assumes that the nodes aresynchronized to a master clock and medium access which istime-based

Adaptive Clustering Lin and Gerla [8] analyzed the role ofsupport of multimedia applications in a general multihop adhoc mobile network using CDMA based medium arbitration[1] To minimize the delivery of data the network is clusteredand a distinct codewould be assigned to the cluster Similar to[6 9] an ID-based selection scheme of clusters is employedLike LCA in this too a one-hop intracluster topology can beestablished A CH decides the codes of communication withthe neighboring CHs This algorithm tries to control the sizeof the cluster optimally by balancing the interest in the reuseof channels spatially which can be enhanced by having smallclusters and a certain data delivery delay which decreasesby bypassing the intercluster routing technique that is largecluster sizes Similarly as in LCA [1] TDMA is used inintracluster communication Each cluster would use a uniquecode resulting in the simple implementation of the sameGreat potential for reaching up to the QoS requirements canbe often found in these multimedia applications

Weighted Clustering Algorithm (WCA) WCA selects a partic-ular node as a CH depending on the number of surroundingneighbors power of transmission battery-life and rate ofmobility of the node [10 11] WCA also restricts the number

of sensor nodes in a particular cluster thereby preventingdegradation of the performance of the MAC protocol

Distributed Clustering Algorithm (DCA) In DCA wirelesssensor nodes are assigned various weights on preset criteriaThe more is the weight of the node the better it would befor playing the role of a CH The major advantage of thistechnique [12] is that by representing the nodes with the helpof certain weights with parameters which are related to themobility of the nodes we can choose to give the role of CHsto those nodes that are better qualified A very interestingresult regarding this is that the complexity pertaining to thetime parameter of the DCA is limited by a parameter of thenetwork that depends on the topology of the network (thatmay change due to mobility of the sensor nodes) rather thanon the network size The DCA [12] is very much apt forclustering ldquoquasi-staticrdquo ad hoc networks

k-Medoids Clustering Algorithm The k-medoids algorithmis related very closely to the k-means algorithm and themedoid shift algorithm k-means and k-medoids algorithmshave the ability to split the WSN to groups and both ofthese algorithms try to minimize the distance between pointsdesignated to be in a cluster and a specific point designatedas the center of that cluster As compared to the k-meansalgorithm k-medoids choose data points as centers (exem-plars) and they work with any arbitrary matrix comprisingof distances between data points [13] k-medoids [14] is aconventional partitioning technique of data clustering whicheasily clusters the 119899-object data set into k clusters knownpreviously A beneficial method of determining k is thesilhouette It is much more tolerant to noise and outliers ascompared to the k-means because it tries to reduce a sum ofpairwise differences instead of a sum of squared Euclideandistances The most commonly known implementation ofthe k-medoids clustering is the Partitioning around Medoids(PAM) algorithm

HEED In [2] the authors have proposed the hybrid energy-efficient distributed (HEED) WSN clustering algorithm toprolong the lifetime of the network It supports scalabledata aggregation In HEED the CHs are probabilisticallychosen based on the parameter called residual energy andthen the sensor nodes join the network clusters accordingto their respective level of power The HEED clustering canbe divided into 3 main stages (1) tentative distribution ofCHs (2) election of CH and iterative balancing of the sameand (3) finalization and establishment ofmembership HEEDis completely distributed All the data has to be transmittedbetween the sensor nodes or known locally [15]

LEACH-C LEACH-C [16] is a modified LEACH usingcentralized clustering control which is the same steady-state phase algorithm as LEACH [16] LEACH-C is differentfrom LEACH only in its setup phase In the setup phasein LEACH-C every wireless sensor node would send infor-mation regarding its current location (probably determinedusing GPS) and its residual energy level to the BSThe BS willthen elect the number of optimal CHs for the network andthen the network is configured into clusters for the current

International Journal of Distributed Sensor Networks 3

round Later the BS would broadcast an advertisementmessage to all the other sensor nodes in the network thismessage would contain the IDs of the various CHs and IDof all the member nodes of a cluster

3 k-Means Clustering Algorithm

k-means is the simplest algorithmused for unsupervised clus-tering This algorithm partitions the data set into k clustersusing the Euclidian distance mean resulting in maximizingintracluster similarity and minimizing intercluster similarityk-means is iterative in nature [17] It follows the followingsteps

(1) Arbitrarily generate 119896 points (cluster centers) [17] 119896being the number of clusters desired

(2) Calculate the distance between each of the data pointsto each of the centers and assign each point to theclosest center

(3) Calculate the new cluster center by calculating themean value of all data points in the respective cluster

(4) With the new centers repeat step (2) [17] If theassignment of cluster for the data points changesrepeat step (3) else stop the process

The distance between the data points is calculated usingEuclidean distance defined by

Dist (1198831 1198832) = radic

119899

sum

119894=1

(1199091119894minus 1199092119894)2

(1)

31 Types of k-Means Clustering in WSNs

311 Centralized k-Means Clustering [17] When a centralauthority makes the various decisions and partitions thegroup of sensor nodes into clusters without the involvementof any other nodes it is defined as the centralized way ofclustering In this type of clustering the centralized authoritygets the necessary information required for carrying out theclustering process from the individual sensor nodes

Cluster Head Selection From [17] among the sensor nodeswhich are at the first level of distance and the next level ofdistance from the centroid we take the nodeswith the highestenergy and select the one which is the nearest as the CH

Declaration of Cluster Head Upon completion of the cluster-ing process by the central node the central node it sends backthe information of its cluster and respective CHs to each andevery node individually [17] Thus every node is aware of itscluster and its CH

312 Distributed k-Means Clustering In this type of clus-tering every node gets all the necessary information forclustering from all other nodes Since the k-means algorithm[17] is based on the basic principle of Euclidian distancesand residual energies of the sensor nodes (for choosing CH)the information of the location of nodes and their respective

residual energies is obtained by every node by exchangingmessages among themselves After collecting the informationabout all the nodes each node runs the algorithm (k-means)The k-means algorithm [17] for clustering and the algorithmfor choosing CH are very much the same as the algorithmsused in centralized clustering As every node runs the samealgorithm every node knows its parent cluster and its CHSo here there is no process of Declaration of Cluster Headas in centralized Thus the distributed clustering process iscomplete

Initially k cluster centers are randomly chosen and eachof the nodes is assigned a point to the nearest center Thenthe clusters are updated by finding the mean of the variousmember patterns and the same steps are repeated untilthe algorithm converges [18] Typical convergence criteriawould include the most number of successive iterations anddifference on the value of the function of distortion [18]

The detailed algorithm (in a WSN scenario) is as follows

(1) Consider the inputs

(i) 119896-number of clusters set of data points (nodelocations) are 119909

1 119909

119899

(ii) Association of119909119894will be done only to one cluster

(iii) 119888(119894) denotes 119894th iteration in the clustering pro-cess

(2) Place 119896 centroids in random places 1198881 119888

119896

119888119896=

sum119894119862(119894)=119896119909119894

119873119896

119896 = 1 119870 (2)

(3) Repeat until convergence

(a) For each point 119909119894

(i) find the nearest centroid

119862 (119894) = argmin1le119896le119870

1003817100381710038171003817119909119894minus 119888119896

1003817100381710038171003817

2

119894 = 1 119873 (3)

(ii) Assign the point 119909119894to centroid 119888

119895which is

at the least distance

(b) For each cluster 119895 = 1 119896

119888119895(119886) =

1

119899119895119909119894rarr119888119895

sum119909119894(119886) for 119886 = 1 119889 (4)

where 119886 is the attribute (numerical) value of thedata set

(i) A new centroid 119888119895= means of all points of

119909119894assigned to cluster 119895 in previous step

(4) Stop when the iterations converge no node changesits cluster in successive iterations


32 Network Model and Radio Energy Model

321 Basic Assumptions In our proposedmodel we assume asensor network model as given in [19] and build upon it withthe following properties

(a) The BS is a high energy node and is located far awayfrom the extremities of the sensor network

(b) The network is homogenous with all sensor nodeshaving the same computational and transmissioncapabilities In other words all nodes are capable ofacting as CH nodes

(c) The sensor nodes have a fixed energy supply withuniform initial energy

(d) The sensor nodes can (if required) vary the powerwith which they transmit signals according to thereceived signal strength indication of a particularnode

(e) The sensor node scans its environment at a fixedrate and will contain data to be sent to the BS at allintervals

(f) We assume that the sensor nodes are stationaryin our study because mobile nodes add extendedcomplexity to the clustering mechanism and theyinvolve knowledge of the geographic location of thenodes

(g) The sensor nodes in general have location informa-tion such as a GPS support or geographic hash tableinformation

(h) The communication takes place over a symmetricpropagation channel

(i) The CHs perform data compression to reduce theamount of bits transmitted to the BS

(j) The sensor nodes are capable of computational func-tions and the algorithm proceeds in a distributedfashion with all nodes individually collecting data

(k) The BS indicates all nodes to reinitiate clusteringwhen all the CH nodes in the network have insuffi-cient energy

322 RadioEnergy Model In the recent history there hasbeen lot of research in the area of ultralow power radios If theassumptions about the radio characteristics like the energydissipation during transmission and reception modes arechanged this will affect the advantages of different algorithms[19] Hence in our study we use the simple first-orderradio model that was used in the LEACH algorithm sothat the results and advantages of the new algorithm can beunderstood

We assume that the radio dissipates 119864elec amount ofenergy to transmit receiver circuitry and 119864amp for the trans-mitter amplifier to achieve an acceptable signal to noise ratioAn inverse squared energy loss is assumed due to channel

Table 1 Energy dissipated by various operations in radio model

Operation Energy dissipatedTransmitter electronics (119864Tx-elec)Receiver electronics (119864Rx-elec)(119864Tx-elec = 119864Rx-elec = 119864elec)

50 nJbit

Transmit amplifier (119864fs)Transmit amplifier (119864mp)

100 pJbitm200013 pJbitm2

Data aggregation and processing (119864DA) 5 nJbitsignal

transmission To transmit a k-bit message for a distance of 119889using the above-proposedmodel [20] the radiowould expend

119864Tx = 119896119864elec + 119896isinfs119889

2 119889 le 119889crossover

119896119864elec + 119896isinmp1198894 119889 gt 119889crossover

(5)

where 119889crossover [20] is the distance after which we switchfrom frissrsquos free space propagation model to multipath fadingmodel This crossover distance is calculated as follows

119889crossover =isinfsisinmp (6)

And to receive the message it will expend

119864Rx (119896) = 119864Rx-elec (119897) = 119896119864elec (7)

Additionally each CH node will aggregate the datapackets received from its 119872 sensor nodes before sendinga single data packet after each communication round Theenergy expended in this process is given by

119872lowast 119864DA lowast 119896 (8)

Table 1 gives the standard values of the parameters asfound in [19 21] For our study we have adopted theseparameters and proceeded with the algorithm design Anyalgorithmrsquos efficiency will be tested by its minimizations oftransmit and receive operations for each message and thedistance between the nodes According to our assumptionsstated above the radio channel is considered symmetric soenergy required for transmitting a message from node A tonode B is the same for transmission from node B to node AWe have also assumed that the sensor nodes will always havek-bit data packets to transmit to the CHs

4 Modified k-Means Algorithm

The modified k-means algorithm (Mk-means) is built uponthe foundation of the k-means algorithm itself with a majormodification to ensure load balancing and extension ofnetwork lifetimeThe algorithm proceeds in a series of logicalsteps similar to k-means and adds a final step after stableclusters have been achieved detailed in Figure 1 schedule ofcluster activity in each cycle where the cycle indicates theremoval of black listed nodes

41 Setup Phase The algorithm begins with a setup phasein which the BS randomly assigns three (119896 = 3) nodesas the initial centroids in the sensing area The remainder


Cluster head 12 active

Cycle 1 Cycle 2 Cycle n

Time

Steady state phaseSetup phase

CH centroid selection

Slot for cluster 1 Slot for cluster 2

Slot for cluster 3



middot middot middot

Figure 1 Schedule of cluster activity in each round

of the clustering setup proceeds in a distributed fashionwith nodes communicating with each other to establish theoptimum means within each initially assigned cluster At theend the final CH node assigns its two nearest nodes as CHstoo Hence in each cluster three nodes act as CHs on a loadsharing basis and distribute the energy dissipation that wouldotherwise have occurred at a single CH node

42 Network Operation Phase After three stable clustershave been established in a distributed fashion amongstall the nodes network operation can proceed This is theoperation area which is of actual interest for time spentduring clustering is a waste as far as data collection andsensing for the application is concerned We have consideredthree variations of this network model in order to firmlyestablish the superiority of the Mk-means algorithm invarious applications and energy saving parameters

(1) A simple network the CH node simply forwards eachdata packet it receives to the BS

(2) A smart networkwith data aggregation a user definedthreshold is established at each sensor node so thatit only sends data selectively The CH node transmitsonly one aggregated packet at the end of each round

(3) A smart network with data aggregation and top-kquery the CH only transmits the user defined top-119896query result to the BS

The clustering exists as long as a predefined energycriterion is met by all nodes within a given cluster If thatcondition is not satisfied reclustering is initiated by the BS

421 Simple Network After the clustering phase stable clus-ters have been established network operation can beginWhen a node is established as the final CH it broadcasts aTDMA frame to all sensor nodes in its cluster The nodescommunicate with the head on the basis of this frame thuseliminating the multiple channel access and data collisionproblem In the simple network we assume that a nodealways has a data packet to send to the CH at every instantAlso the CH node immediately forwards the data packetto the BS An important issue faced here is the rotation ofthe multiple CH nodes in each cluster Even though thereare three CH nodes for every node cluster only one nodeacts as a CH at a time We have implemented a CH rotation

mechanism based on load received that is number oftransmissions After every round of communication the CHnode is switched to one of the other nodes in the cluster andthis information is broadcasted to the network Additionallywhen a CH node is not acting as a CH node it acts as asimple sensor forwarding data to the currently active CHnode We define one round of communication as each sensornode within the network transmitting its data to its CH

Smart Network In this network scenario we establish auser defined data filter threshold at each sensor node Thisapproach is similar to that in Filter Based Aggregation(FILA) [22] In this approach we establish a threshold (eventtriggered) at each sensor node For example if the nodes aredeployed for a fire detection application and the parameterbeing measured is temperature If we establish a threshold of100 degrees at each node this means that the sensor node willonly transmit data to its CH node if it senses a temperaturevalue above 100 degrees Based on user defined applicationspecific threshold values sensed data is reported Applicationof a smart network ensures that we suppress the transmissionof unnecessary data to the CHnodes By establishing the filterat the sensor node the burden on the CH node is reduced toaggregate and separate data based on the threshold

In this mechanism the CH still transmits all data packetsthat it receives directly to the BS However the networkoperation will last for a longer duration as at every instanta sensor node may or may not send a data packet to theBS This way for every communication round the CH nodewill receive a lower number of data packets than the simplenetwork Hence it will need to expend less energy per roundfor data transmission and this will significantly increase theamount of time that each CH node in the network will lastThis will also ensure that we break the clustering mechanismlater than in the simple network therefore leading to morestable clusters and longer network operation

Smart Network with Top-119896 Query The top-k query [23] isan application based query mechanism in which the userrequests the top-k data values of one or more sensingparameters from the network in order to make a decisionIn this network model we again follow the FILA [22] basedmechanism for implementation of the query The thresholdat each node still remains and we establish a data aggregationmodel at each CH node along with a global user defined top-119896 query

For data aggregation the CH node does not send eachdata packet as it is received Each CH waits for a roundof communication to finish aggregates all the data packetsreceived by it into a single data packet and transmits thisdata packet to the BS It then passes the CH duties to the nextCH node The energy required to aggregate data packets issignificantly lower than the energy required for transmissionTherefore in this methodology we further lower the energyconsumption at each layer of the network and enhancenetwork lifetime

Within the aggregated data packet sent to the BS afterevery round the CH computes and includes the result ofthe top-k query These transmissions result in a databaseestablished at the BS which contains the top-k query result


and respective node id for each cluster for each round duringnetwork operation

For each of the three methodologies described abovethere were two important considerations

(1) When to break the network operation and reclusterthe nodes

(2) How to deal with nodes that die during networkoperation

For the first condition if any one of the CH nodes ina cluster falls below this threshold the remaining two CHsdivide the load amongst them and continue network opera-tion The CH node which falls below the threshold continuesto act as a sensor node and sends data to the remaining CHnodes according to the TDMA frame allocatedThe thresholddefined for a node to act as a CH is 70 of its initial batteryenergy at the time of becoming CH The network operationbreaks and reclustering is initiated when all three CH nodesin any of the clusters are incapable of acting as such andthe last node sends a message to the BS which initiates theclustering process as described in the setup phase

Another important feature of theMk-means algorithm isan inherent 3-2-1 clustermechanismDuring themultiple CHselection there is no restriction on the CH node to choosea node from within its own cluster to act as the additionalCH While this will not make much difference during thenormal network operation it will be useful during the finalstages when a majority of the nodes are unavailable to actas CH nodes only one large cluster will be formed witheach of the multiple CH nodes spread across the networkTherefore it will be similar to the k-means operation inwhichthree clusters are formed with a single CH In this topologyhowever the network operation will only be suspended whenall three nodes are unable to act as CH nodes due to a fall inbattery energy below the prespecified threshold

43 Postclustering Phase This phase very rarely occurs inthe Mk-means algorithm because of the high stability of theclusters and hence longer network operation In this stage nonode in the network has energy sufficient to act as a CHnodeThe criterion taken for this is that if 65 of the nodes alive areblacklisted the network will move to this phase

From the battery power discharge profile [24 25] itis found that the stability of the battery to support theoperations after losing its 70 of initial energy weakens andit starts to discharge at rapid phase Hence the clusteringprocess is stopped and direct transmission is initiated so thatthe nodes will not waste their energy in forming new clustersinstead they can send useful data to BS

To simulate a realistic environmental scenario we havenot stopped the simulation of the network when none of thenodes in it are unfit for becoming CH owing to a paucity ofbattery energy In this phase all the remaining alive nodesin the network start sending their data directly to the BSThese highly expensive energy transmissions continue till80 of the network nodes die at which point the networkbecomes useless in terms of the useful data it can provide (seeAlgorithm 1)

Table 2 Simulation parameters

Parameter ValueSimulation area 100m times 100mInitial energy per node (119864init) 2 JNodes 100Data size 2000 bitsBase station (BS) location (50m 175m)119864Elec 50 nJbitTransmission amplifier type 119864fs 10 pJbitm2

Transmission amplifier type 119864mp 00013 pJbitm2

Data aggregation energy 5 nJbitsignalEnergy threshold (ethres) 07 lowast 119864init

Break parameter 65 of nodesblacklisted

5 Simulations and Analysis of Results

51 Simulation Environment All the experiments are con-ducted for the proposed Mk-means algorithm versus k-means clustering LEACH LEACH-C HEED SECA ECRAPAGASIS and NCACM using MATLAB version R2012b andC programming language [19 26ndash29] Each sensor node wasassumed to have initial energy of 2 J In the simulation runwe used the following parameter values same as in [26] asshown in Table 2

52 Simulation Metrics and Analysis In order to suitablycompare the performance of the Mk-means algorithm withthe k-means algorithm we have taken a number of metrics incommon with the work of [21 26] There are two importantparameters in the simulation One is the energy thresholdand the other is the break parameter The energy thresholdis defined at each CH If the energy of the node falls belowthe threshold value it is no longer fit to act as a CH Thisparameter is fixed at 70 of the initial battery energy or14 J through empirical observations The break parameteris defined as the number of blacklisted nodes that causethe network to break from the network operation phaseand move to the postclustering phase Through empiricalobservations this parameter was fixed at 65of nodesWhenthese many nodes are blacklisted the network breaks tothe postclustering phase where all nodes start sending datadirectly to the BS

All the results discussed below are for Mk-means and k-means algorithms with a smart network and top-k based dataaggregation model The results have been shown for 10 runsof the code

521 Increase in Network Lifetime and Effective Data SentTheeffective lifetime of a sensor network is an importantmet-ric to judge the usefulness and performance of the networkAn inherent problem with MATLAB v R2012b simulation isthat an accurate model for time cannot be integrated intothe simulation scenario to objectively measure the networklifetime in hours or days Therefore we have used the totalnumber of transmissions throughout the network operation


For Smart Network with Top-119896Clustering Phase

Function 1for 119894 = 1 nodesfor 119895 = 1 119899 (CH nodes)

data generation at each node threshold established globally establishes a TDMA frameFunction 2 transmission from each sensor node to its respective CH after threshold check CH data aggregation after each round calculation of top-119896 result and transmission to BS

For dead nodesFunction 3

checks each nodes energy against 0 to establish node dying removes dead nodes from all lists including blacklist

CH rotation mechanism after each round of communication collect energy spend for transmission and reception check the Cthreshold of rotated CH to satisfy the criteria if fails current CH calls to next CH as per schedule and informs BS check atleast one CH in each cluster at BS if this criteria fails call Function 1call Function 2 again

For post clustering phaseFunction 4

checks each nodes energy against 0 to establish node dying after each round removes dead nodes from all lists including blacklist

Function 5for 119894 = 1 119899 (alive nodes) all nodes send data directly to BS energy deductions due to transmission and reception

Algorithm 1

as an indicator of the overall lifetime of the network Thismetric is not indicative of the number of hours or days thenetwork might exist but it is an indirect way of gauging howmuch longer the Mk-means algorithm allows the networkto function over the k-means algorithm The number oftransmissions is used interchangeably as time over the courseof this discussion

FromFigure 2 we observe that the average increase of thenumber of rounds of communication over 10 runs of code is33 times This metric is indicative of the substantial increasein the number of times each sensor node in the network isallowed to send data before reclustering is initiated

Additionally the total number of data transmissionsthat took place in the network has also been measured toconclusively establish thatMk-means results in clusterswhichare stable and remain in operation for longer periods oftime with nodes in each cluster being able to send a lot ofdata before clustering is reinitiated This metric is a directmeasure of the number of data packets that were sent to theBS during the operation of the network It represents theincrease in useful data traffic which is the most essential partof a networkrsquos lifetime

From Figure 3 we can observe that over 10 runs of thecode the Mk-means algorithm outperforms the k-meansalgorithm significantly At worst a 61 increase was observedand 188 as the maximum increase in traffic supportedOn average the overall increase in network transmissions

3172

43473937

4711

3791

4603 4444

37734162 4072

361 344 390 326 361 411 391 370 385 394

1 2 3 4 5 6 7 8 9 10Runs of code

k-meansMk-means

0500

100015002000250030003500400045005000

Roun

ds

Figure 2 Rounds of communication inMk-means versus 119896-means

was found to be 136 This metric shows that Mk-meanssignificantly increases the lifetime of the sensor network ascompared to k-means

Besides this there are several other metrics which weregauged in order to determine the extension of the networklifetime throughMk-means For instance we have measuredthe number of rounds of communication that occurred


116

136

178

93

165

137

171

61

188

110

1 2 3 4 5 6 7 8 9 10

Incr

ease

()

Runs of code

0

20

40

60

80

100

120

140

160

180

200

Figure 3 Total increase in transmissions on Mk-means versus k-means

2338

3559

2829

4073

28443084 3281

2864 2989 2945

1 2 3 4 5 6 7 8 9 10Runs of code

0

50

100

150

200

250

300

350

400

450

()

Figure 4 Percentage increase in data transmissions

during the network operation phaseThis is a standardmetricand can be used to directly establish that the Mk-meansalgorithm results as shown in Figure 4 on much more stableclusters than the k-means algorithm which last much longerand hence allow more number of useful data transmissionsduring the network operation phase We define a round ofcommunication as when all of the nodes in the network havehad an opportunity to send data to their respective CH node

Thefinal parameter used is the number of times clusteringis done in both Mk-means and k-means This parameterestablishes that Mk-means spends much less time duringthe clustering process than k-means does This is a directconsequence of stable clusters being formed in Mk-meansas compared to k-means Clustering is generally the mostexpensive process in the network as a huge number oftransmissions have to be made to and from each node TheMk-means algorithm minimizes the number of clusteringprocesses that have to be undertaken during network oper-ation

On average the Mk-means algorithm undertakes theclustering process 17 times while k-means does it 55 times

1518

1520

14 1518 19

1519

5559

5560

5651

54 54 52 53

Num

ber o

f clu

sterin

g pr

oces

ses

1 2 3 4 5 6 7 8 9 10Runs of code

k-meansMk-means

0

10

20

30

40

50

60

70

Figure 5 Total number of clustering processes inMk-means versusk-means

as shown in Figure 5This represents a significant decrease inthe amount number of transmissions that the network has tomake during clustering As established before clustering is anexpensive process and the decrease is a significant one thusfurther conserving energy at the nodes and further extendingnetwork lifetime

522 Number of Nodes Alive The number of nodes alive isa well-established standard metric to measure the lifetimeof a sensor network An important parameter in this metricis the FND or First Node Dead metric which measures therounds of communication till the death of the first node inthe network

From Figure 6 the average number of rounds of com-munication after which the first node dies in Mk-means is1441 and the average for k-means is 373 The introductionof a filter at the node level to suppresses unnecessary datatransmissions the rotation of multiple CHs in a cluster byload and the application of a data aggregation model greatlyprolong the FND criterion in Mk-means as compared to k-means with the same parameters This is again due to thestability of the Mk-means clusters as compared to the k-means clusters

523 Average Energy of the Network The average energy dis-sipation here is plotted in pairs using the followingmethodol-ogyThe energy graph consists of pairs each pair representingone clustering process and one successive network run till theclustering process breaksThe first bar of each pair representsthe energy at the start of that clustering process The next barrepresents the energy at the start of the network operationphase Thus the fall between the bars represents the amountof energy dissipated during clustering The fall betweensuccessive pairs represents the amount of energy that wasdissipated in the previous network run The sharper this fallthe more energy is dissipated during the network indicatingthat the network ran for a significant amount of time Having


9081080 1089

2490

2012

1039 1020

2251

1512

1013

361 344 390 326 361 411 391 394 370 385

1 2 3 4 5Runs of code

6 7 8 9 10

Roun

ds o

f com

mun

icat

ion

k-meansMk-means

0

500

1000

1500

2000

2500

3000

Figure 6 First Node Dead

Mk-means

Ener

gy (J

)

150100500

Rounds

2

19

18

17

16

15

14

13

12

11

1

Figure 7 Average energy dissipation inMk-means

already established that Mk-means forms a fewer number ofhighly stable clusterswith a significant increase inmeaningfuldata transmissionwe therefore establish that this fall betweenpairs is further indication of the longevity of each networkoperation phase

Once the postclustering phase is initiated the energy iscalculated after every round of communication

As observed from Figure 7 the fall between pairs is verysharp indicating the longevity of the network The breakbetween the network operation phase and the postclusteringphase is clearly visible on the graph

We can contrast this energy graph with a similar plot fork-means as shown in Figure 8 There are significantly morepairs visible in this graph owing to the greater number ofclustering processes that occur in k-means as compared toMk-means Further the fall between the pairs is hardly visiblewhich is indicative of the fact that the k-means clusters areunstable as compared to Mk-means and decay much fasterforcing the network to initiate the reclustering process moreoften

k-means

Rounds1009080706050403020100

0

02

04

06

08

1

12

14

16

18

2

Ener

gy (J

)

Figure 8 Average energy dissipation in k-means

60

122

219

335358

513

LEAC

H

HEE

D

LEAC

H-C

SECA

0

100

200

300

400

500

600

Roun

ds o

f com

mun

icat

ion

Mk

-mea

ns

k-m

eans

Figure 9 First Node Dead comparison for validation

524 Validation and Comparison In order to verify the sim-ulation results discussed above the base k-means algorithmwas cross referenced against standards as in [26 30 31]Our proposed Mk-means algorithm is built upon the samemethodology as the k-means algorithm Comparing theMk-means and the k-means codes the results for the FND (FirstNode Dead) metric are against the results cited in [26] Asexpected the k-means code performs poorly due to the highdegree of energy dissipation and the lack of any sensor filtertechnique This is due to its inability to form stable CHs andthe small number of sensor nodes The Mk-means due toits inherently stable clustering phenomenon performs welljust by outstripping both LEACH and HEED and k-meansalgorithm alone as shown in Figure 9

But in later case the Mk-means algorithm with top-k query dramatically outperforms the existing algorithmsowing to its unique multiple CH methodology as shownin Figures 10 and 11 The rotation of CHs based on load


150 161 188255

390 455530 566

1441

LEAC

H

LEAC

H-E

NCA

CM

HEE

D

LEAC

H-C

PEG

ASI

S

SECA

-M

ECRA

Mk

-mea

ns

0

200

400

600

800

1000

1200

1400

1600

Roun

ds o

f com

mun

icat

ion

Figure 10 First Node Dead comparison

375 382 405614

968 997 1089 1195

4054

LEAC

H

LEAC

H-E

NCA

CM

HEE

D

LEAC

H-C

PEG

ASI

S

SECA

-M

ECRA

Mk

-mea

ns

0500

10001500200025003000350040004500

Roun

ds o

f com

mun

icat

ion

Figure 11 Half of the nodes alive

and the filter based threshold attached to each sensor nodeensures that the energy dissipation in the network is mini-mal Additionally clustering processes are minimized whichfurther reduces the energy dissipation The data aggregationmodel reduces the number of transmissions that a CH nodehas to make thereby reducing the number of times a veryexpensive energy consuming process needs to be performedAnd it shows that the about 300 of rise in sensor node lifetime is due to the factor that 3 CHs are elected per clusterwhich scales down the energy dissipation by one-third in theprocess of reclustering and implementation of query baseddata forwarding

The performance comparison is done with 100 sensornodes in a sensing area about 100m times 100m for 1200 roundsof communication A round is considered to be the activeperiod of one CH in the cluster The results were plottedin Figure 12 residual energy of the network against roundFrom the simulations results it is found that our proposedscheme Mk-means with top-k query takes the advantages ofhigher residual energy throughout the simulation with stable

0 200 400 600 800 1000 1200Rounds

Mk-meansECRASECA-M

k-meansHEEDLEACH

0

05

1

15

2

25

Ener

gy (J

)

Figure 12 Total network energy

clusters and reduced energy consumption than that of ECRASECA-M k-means HEED and LEACH

6 Conclusion

We analyzed the performance of the proposed Mk-meansalgorithm versus the k-means and other standard algorithmsIn order to suitably compare the performance of the Mk-means algorithm with the k-means algorithm a number ofmetrics were measured Mk-means significantly increasedthe lifetime of the sensor network as compared to k-meansThe number of times each sensor node in the network wasallowed to send data before reclustering is initiated was foundto be more in Mk-means than in k-means The Mk-meansalgorithmminimizes the number of clustering processes thathave to be undertaken during network operationMk-meanswas found to significantly decrease the amount numberof transmissions that the network had to make duringclustering To conclude theMk-means algorithm was foundto outperform the existing clustering algorithms owing to itsuniquemultiple CHmethodologyThe rotation of CHs basedon load and the filter based threshold attached to each sensornode was found to ensure that the energy dissipation in thenetwork is minimal Additionally clustering processes werefound to be minimized which further reduced the energydissipation

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] A A Abbasi andM Younis ldquoA survey on clustering algorithmsfor wireless sensor networksrdquo Computer Communications vol30 no 14-15 pp 2826ndash2841 2007


[2] O Younis and S Fahmy ldquoHEED a hybrid energy-efficientdistributed clustering approach for ad-hoc sensor networksrdquoIEEE Transactions on Mobile Computing vol 3 no 4 pp 366ndash379 2004

[3] S Yi J Heo Y Cho and J Hong ldquoPEACH power-efficientand adaptive clustering hierarchy protocol for wireless sensornetworksrdquo Computer Communications vol 30 no 14-15 pp2842ndash2852 2007

[4] W-T Su K-M Chang and Y-H Kuo ldquoeHIP an energy-efficient hybrid intrusion prohibition system for cluster-basedwireless sensor networksrdquoComputer Networks vol 51 no 4 pp1151ndash1168 2007

[5] V Mhatre and C Rosenberg ldquoDesign guidelines for wirelesssensor networks communication clustering and aggregationrdquoAd Hoc Networks vol 2 no 1 pp 45ndash63 2004

[6] D J Baker and A Ephremides ldquoThe architectural organizationof a mobile radio network via a distributed algorithmrdquo IEEETransactions on Communications vol 29 no 11 pp 1694ndash17011981

[7] D J Baker A Ephremides and J A Flynn ldquoThe design andsimulation of a mobile radio network with distributed controlrdquoIEEE Journal on Selected Areas in Communications vol 2 no 1pp 226ndash237 2003

[8] C R Lin andM Gerla ldquoAdaptive clustering for mobile wirelessnetworksrdquo IEEE Journal on Selected Areas in Communicationsvol 15 no 7 pp 1265ndash1275 1997

[9] A Ephremides J E Wieselthier and D J Baker ldquoA designconcept for reliable mobile radio networks with frequencyhopping signalingrdquo Proceedings of the IEEE vol 75 no 1 pp56ndash73 1987

[10] M Chatterjee S K Das and D Turgut ldquoWCA a weightedclustering algorithm for mobile ad hoc networksrdquo ClusterComputing vol 5 no 2 pp 193ndash204 2002

[11] S Bandyopadhyay and E J Coyle ldquoAn energy efficient hier-archical clustering algorithm for wireless sensor networksrdquo inProceedings of the 22nd Annual Joint Conference on the IEEEComputer and Communications Societies (INFOCOM rsquo03) vol3 pp 1713ndash1723 IEEE April 2003

[12] S Basagni ldquoDistributed clustering for ad hoc networksrdquo inProceedings of the 4th International Symposium on ParallelArchitectures Algorithms and Networks (I-SPAN rsquo99) pp 310ndash315 IEEE Perth Australia June 1999

[13] L Kaufman and P J Rousseeuw ldquoClustering by means ofMedoidsrdquo in Statistical Data Analysis Based on the L1-Normand Related Methods pp 405ndash416 North-Holland PublishingCompany 1987

[14] S Shah andM Singh ldquoComparison of a time efficient modifiedK-mean algorithm with K-mean and K-medoid algorithmrdquo inProceedings of the International Conference on CommunicationSystems and Network Technologies (CSNT rsquo12) pp 435ndash437Rajkot India May 2012

[15] R E BlaceM Eltoweissy andWAbd-Almageed ldquoThreat awareclustering in wireless sensor networksrdquo in Proceedings of theIFIP Conference on Wireless Sensor and Actor Networks (WSANrsquo08) pp 1ndash12 Ottawa Canada July 2008

[16] S D Muruganathan D C F Ma R I Bhasin and A OFapojuwo ldquoA centralized energy-efficient routing protocol forwireless sensor networksrdquo IEEECommunicationsMagazine vol43 no 3 pp S8ndashS13 2005

[17] P Sasikumar and S Khara ldquoK-means clustering in wirelesssensor networksrdquo in Proceedings of the IEEE 4th International

Conference on Computational Intelligence and CommunicationNetworks (CICN rsquo12) pp 140ndash144 Mathura India November2012

[18] X Jin S Kim J Han L Cao and Z Yin ldquoGAD general activitydetection for fast clustering on large datardquo in Proceedings of theSIAM International Conference on Data Mining (SDM rsquo09) pp2ndash13 Sparks Nev USA April 2009

[19] W R Heinzelman A Chandrakasan and H Balakrish-nan ldquoEnergy-efficient communication protocol for wirelessmicrosensor networksrdquo in Proceedings of the 33rd AnnualHawaii International Conference on SystemSciences (HICSS rsquo00)IEEE Maui Hawaii USA January 2000

[20] WNWMuhamad K Dimyati RMohamad et al ldquoEvaluationof Stable Cluster Head Election (SCHE) routing protocol forwireless sensor networksrdquo in Proceedings of the IEEE Interna-tional RF and Microwave Conference (RFM rsquo08) pp 101ndash105IEEE Kuala Lumpur Malaysia December 2008

[21] W Xiaoping L Hong and L Gang ldquoAn improved routingalgorithm based on LEACH protocolrdquo in Proceedings of the9th International Symposium on Distributed Computing andApplications to Business Engineering and Science (DCABES rsquo10)pp 259ndash262 IEEE Hong Kong August 2010

[22] S MaddenM J Franklin J M Hellerstein andWHong TAGA Tiny AGgregation Service for Ad-Hoc Sensor Networks UCBerkeley and Intel Research Berkeley Calif USA 2002

[23] HHaiping F JuanW Ruchuan andQ XiaoLin ldquoAn exact top-k query algorithm with privacy protection in wireless sensornetworksrdquo International Journal of Distributed Sensor Networksvol 2014 Article ID 749049 10 pages 2014

[24] A Silva M Liu and M Moghaddam ldquoPower-managementtechniques for wireless sensor networks and similar low-powercommunication devices based on nonrechargeable batteriesrdquoJournal of Computer Networks and Communications vol 2012Article ID 757291 10 pages 2012

[25] S Barcellona M Brenna F Foiadelli M Longo and L PiegarildquoAnalysis of ageing effect on Li-polymer batteriesrdquoThe ScientificWorld Journal vol 2015 Article ID 979321 8 pages 2015

[26] J-Y Chang and P-H Ju ldquoAn energy-saving routing architecturewith a uniform clustering algorithm for wireless body sensornetworksrdquo Future Generation Computer Systems vol 35 pp128ndash140 2014

[27] P Kuila and P K Jana ldquoA novel differential evolution basedclustering algorithm for wireless sensor networksrdquo Applied SoftComputing Journal vol 25 pp 414ndash425 2014

[28] P Kuila and P K Jana ldquoEnergy efficient clustering and rout-ing algorithms for wireless sensor networks particle swarmoptimization approachrdquo Engineering Applications of ArtificialIntelligence vol 33 pp 127ndash140 2014

[29] T K Jain D S Saini and S V Bhooshan ldquoCluster headselection in a homogeneous wireless sensor network ensuringfull connectivity with minimum isolated nodesrdquo Journal ofSensors vol 2014 Article ID 724219 8 pages 2014

[30] J R Patole and J Abraham ldquoDesign of MAP-REDUCEand K-MEANS based network clustering protocol for sensornetworksrdquo in Proceedings of the 3rd International Conferenceon Computing Communication and Networking Technologies(ICCCNT rsquo12) pp 1ndash5 IEEE Coimbatore India July 2012

[31] J-Y Chang and P-H Ju ldquoAn efficient cluster-based powersaving scheme for wireless sensor networksrdquo EURASIP Journalon Wireless Communications and Networking vol 2012 article172 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



2 Literature Survey

The last few years have witnessed a rapid increase inthe interest in the usage of WSN in various applicationslike disaster management habitat monitoring and militarysurveillance The sensor nodes in these environments weredeployed randomly and expected to operate independentlyin unsupervised area In this larger number of sensor nodesscalability is addressed by generally grouping the sensornodes intomultiple nonoverlapping clusters In [1] a detailedtaxonomy and generalized classification of various clusteringschemes were presented

The clustering process aims to extend the lifespan ofsensor nodes [2ndash5] Thereby by increasing the lifetime of theCH onewill be able tominimize the need for reclustering andless number of overheads exchanged between a microsensornode and CH The real challenge considered in the field ofclustering algorithms is how to influence the longevity ofsensor nodes in aWSN through comparison of initial energywith the residual energy of the node during each cycle orroundof communication [3] To simplify the depleted batterycauses the sensor nodes to fail soon

Linked Cluster Algorithm (LCA) Baker and Ephremides [6 7]are the first authors to consider clustering in WSN Theyfocused on creating an efficient topology of network thathad the capability to handle the mobility of the nodes Byperforming network clustering [1] the CHs are expected toform a backbone network to which cluster members canconnect while on the move The objective of the proposeddistributed algorithm is to form many clusters such that aCH is independently connected to all the sensor nodes in itsown cluster LCA is thus designed to maximize connectivityof the network But this algorithm assumes that the nodes aresynchronized to a master clock and medium access which istime-based

Adaptive Clustering Lin and Gerla [8] analyzed the role ofsupport of multimedia applications in a general multihop adhoc mobile network using CDMA based medium arbitration[1] To minimize the delivery of data the network is clusteredand a distinct codewould be assigned to the cluster Similar to[6 9] an ID-based selection scheme of clusters is employedLike LCA in this too a one-hop intracluster topology can beestablished A CH decides the codes of communication withthe neighboring CHs This algorithm tries to control the sizeof the cluster optimally by balancing the interest in the reuseof channels spatially which can be enhanced by having smallclusters and a certain data delivery delay which decreasesby bypassing the intercluster routing technique that is largecluster sizes Similarly as in LCA [1] TDMA is used inintracluster communication Each cluster would use a uniquecode resulting in the simple implementation of the sameGreat potential for reaching up to the QoS requirements canbe often found in these multimedia applications

Weighted Clustering Algorithm (WCA) WCA selects a partic-ular node as a CH depending on the number of surroundingneighbors power of transmission battery-life and rate ofmobility of the node [10 11] WCA also restricts the number

of sensor nodes in a particular cluster thereby preventingdegradation of the performance of the MAC protocol

Distributed Clustering Algorithm (DCA) In DCA wirelesssensor nodes are assigned various weights on preset criteriaThe more is the weight of the node the better it would befor playing the role of a CH The major advantage of thistechnique [12] is that by representing the nodes with the helpof certain weights with parameters which are related to themobility of the nodes we can choose to give the role of CHsto those nodes that are better qualified A very interestingresult regarding this is that the complexity pertaining to thetime parameter of the DCA is limited by a parameter of thenetwork that depends on the topology of the network (thatmay change due to mobility of the sensor nodes) rather thanon the network size The DCA [12] is very much apt forclustering ldquoquasi-staticrdquo ad hoc networks

k-Medoids Clustering Algorithm The k-medoids algorithmis related very closely to the k-means algorithm and themedoid shift algorithm k-means and k-medoids algorithmshave the ability to split the WSN to groups and both ofthese algorithms try to minimize the distance between pointsdesignated to be in a cluster and a specific point designatedas the center of that cluster As compared to the k-meansalgorithm k-medoids choose data points as centers (exem-plars) and they work with any arbitrary matrix comprisingof distances between data points [13] k-medoids [14] is aconventional partitioning technique of data clustering whicheasily clusters the 119899-object data set into k clusters knownpreviously A beneficial method of determining k is thesilhouette It is much more tolerant to noise and outliers ascompared to the k-means because it tries to reduce a sum ofpairwise differences instead of a sum of squared Euclideandistances The most commonly known implementation ofthe k-medoids clustering is the Partitioning around Medoids(PAM) algorithm

HEED In [2] the authors have proposed the hybrid energy-efficient distributed (HEED) WSN clustering algorithm toprolong the lifetime of the network It supports scalabledata aggregation In HEED the CHs are probabilisticallychosen based on the parameter called residual energy andthen the sensor nodes join the network clusters accordingto their respective level of power The HEED clustering canbe divided into 3 main stages (1) tentative distribution ofCHs (2) election of CH and iterative balancing of the sameand (3) finalization and establishment ofmembership HEEDis completely distributed All the data has to be transmittedbetween the sensor nodes or known locally [15]

LEACH-C LEACH-C [16] is a modified LEACH usingcentralized clustering control which is the same steady-state phase algorithm as LEACH [16] LEACH-C is differentfrom LEACH only in its setup phase In the setup phasein LEACH-C every wireless sensor node would send infor-mation regarding its current location (probably determinedusing GPS) and its residual energy level to the BSThe BS willthen elect the number of optimal CHs for the network andthen the network is configured into clusters for the current










Dist (1198831 1198832) = radic

119899

sum

119894=1

(1199091119894minus 1199092119894)2

(1)











1 119909

119899




119896

119888119896=

sum119894119862(119894)=119896119909119894

119873119896

119896 = 1 119870 (2)




119862 (119894) = argmin1le119896le119870

1003817100381710038171003817119909119894minus 119888119896

1003817100381710038171003817

2

119894 = 1 119873 (3)


119895which is



119888119895(119886) =

1

119899119895119909119894rarr119888119895

sum119909119894(119886) for 119886 = 1 119889 (4)























50 nJbit





119864Tx = 119896119864elec + 119896isinfs119889



(5)




119864Rx (119896) = 119864Rx-elec (119897) = 119896119864elec (7)


119872lowast 119864DA lowast 119896 (8)








Time




Slot for cluster 3
















































Algorithm 1





3172

43473937

4711

3791

4603 4444

37734162 4072

361 344 390 326 361 411 391 370 385 394

1 2 3 4 5 6 7 8 9 10Runs of code

k-meansMk-means

0500

100015002000250030003500400045005000

Roun

ds





116

136

178

93

165

137

171

61

188

110

1 2 3 4 5 6 7 8 9 10

Incr

ease

()

Runs of code

0

20

40

60

80

100

120

140

160

180

200


2338

3559

2829

4073

28443084 3281

2864 2989 2945

1 2 3 4 5 6 7 8 9 10Runs of code

0

50

100

150

200

250

300

350

400

450

()





1518

1520

14 1518 19

1519

5559

5560

5651

54 54 52 53

Num

ber o

f clu

sterin

g pr

oces

ses

1 2 3 4 5 6 7 8 9 10Runs of code

k-meansMk-means

0

10

20

30

40

50

60

70







9081080 1089

2490

2012

1039 1020

2251

1512

1013

361 344 390 326 361 411 391 394 370 385


6 7 8 9 10

Roun

ds o

f com

mun

icat

ion

k-meansMk-means

0

500

1000

1500

2000

2500

3000


Mk-means

Ener

gy (J

)

150100500

Rounds

2

19

18

17

16

15

14

13

12

11

1






k-means

Rounds1009080706050403020100

0

02

04

06

08

1

12

14

16

18

2

Ener

gy (J

)


60

122

219

335358

513

LEAC

H

HEE

D

LEAC

H-C

SECA

0

100

200

300

400

500

600

Roun

ds o

f com

mun

icat

ion

Mk

-mea

ns

k-m

eans





150 161 188255

390 455530 566

1441

LEAC

H

LEAC

H-E

NCA

CM

HEE

D

LEAC

H-C

PEG

ASI

S

SECA

-M

ECRA

Mk

-mea

ns

0

200

400

600

800

1000

1200

1400

1600

Roun

ds o

f com

mun

icat

ion


375 382 405614

968 997 1089 1195

4054

LEAC

H

LEAC

H-E

NCA

CM

HEE

D

LEAC

H-C

PEG

ASI

S

SECA

-M

ECRA

Mk

-mea

ns

0500

10001500200025003000350040004500

Roun

ds o

f com

mun

icat

ion




0 200 400 600 800 1000 1200Rounds

Mk-meansECRASECA-M

k-meansHEEDLEACH

0

05

1

15

2

25

Ener

gy (J

)



6 Conclusion




References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















Dist (1198831 1198832) = radic

119899

sum

119894=1

(1199091119894minus 1199092119894)2

(1)











1 119909

119899




119896

119888119896=

sum119894119862(119894)=119896119909119894

119873119896

119896 = 1 119870 (2)




119862 (119894) = argmin1le119896le119870

1003817100381710038171003817119909119894minus 119888119896

1003817100381710038171003817

2

119894 = 1 119873 (3)


119895which is



119888119895(119886) =

1

119899119895119909119894rarr119888119895

sum119909119894(119886) for 119886 = 1 119889 (4)























50 nJbit





119864Tx = 119896119864elec + 119896isinfs119889



(5)




119864Rx (119896) = 119864Rx-elec (119897) = 119896119864elec (7)


119872lowast 119864DA lowast 119896 (8)








Time




Slot for cluster 3
















































Algorithm 1





3172

43473937

4711

3791

4603 4444

37734162 4072

361 344 390 326 361 411 391 370 385 394

1 2 3 4 5 6 7 8 9 10Runs of code

k-meansMk-means

0500

100015002000250030003500400045005000

Roun

ds





116

136

178

93

165

137

171

61

188

110

1 2 3 4 5 6 7 8 9 10

Incr

ease

()

Runs of code

0

20

40

60

80

100

120

140

160

180

200


2338

3559

2829

4073

28443084 3281

2864 2989 2945

1 2 3 4 5 6 7 8 9 10Runs of code

0

50

100

150

200

250

300

350

400

450

()





1518

1520

14 1518 19

1519

5559

5560

5651

54 54 52 53

Num

ber o

f clu

sterin

g pr

oces

ses

1 2 3 4 5 6 7 8 9 10Runs of code

k-meansMk-means

0

10

20

30

40

50

60

70







9081080 1089

2490

2012

1039 1020

2251

1512

1013

361 344 390 326 361 411 391 394 370 385


6 7 8 9 10

Roun

ds o

f com

mun

icat

ion

k-meansMk-means

0

500

1000

1500

2000

2500

3000


Mk-means

Ener

gy (J

)

150100500

Rounds

2

19

18

17

16

15

14

13

12

11

1






k-means

Rounds1009080706050403020100

0

02

04

06

08

1

12

14

16

18

2

Ener

gy (J

)


60

122

219

335358

513

LEAC

H

HEE

D

LEAC

H-C

SECA

0

100

200

300

400

500

600

Roun

ds o

f com

mun

icat

ion

Mk

-mea

ns

k-m

eans





150 161 188255

390 455530 566

1441

LEAC

H

LEAC

H-E

NCA

CM

HEE

D

LEAC

H-C

PEG

ASI

S

SECA

-M

ECRA

Mk

-mea

ns

0

200

400

600

800

1000

1200

1400

1600

Roun

ds o

f com

mun

icat

ion


375 382 405614

968 997 1089 1195

4054

LEAC

H

LEAC

H-E

NCA

CM

HEE

D

LEAC

H-C

PEG

ASI

S

SECA

-M

ECRA

Mk

-mea

ns

0500

10001500200025003000350040004500

Roun

ds o

f com

mun

icat

ion




0 200 400 600 800 1000 1200Rounds

Mk-meansECRASECA-M

k-meansHEEDLEACH

0

05

1

15

2

25

Ener

gy (J

)



6 Conclusion




References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



























50 nJbit





119864Tx = 119896119864elec + 119896isinfs119889



(5)




119864Rx (119896) = 119864Rx-elec (119897) = 119896119864elec (7)


119872lowast 119864DA lowast 119896 (8)








Time




Slot for cluster 3
















































Algorithm 1





3172

43473937

4711

3791

4603 4444

37734162 4072

361 344 390 326 361 411 391 370 385 394

1 2 3 4 5 6 7 8 9 10Runs of code

k-meansMk-means

0500

100015002000250030003500400045005000

Roun

ds





116

136

178

93

165

137

171

61

188

110

1 2 3 4 5 6 7 8 9 10

Incr

ease

()

Runs of code

0

20

40

60

80

100

120

140

160

180

200


2338

3559

2829

4073

28443084 3281

2864 2989 2945

1 2 3 4 5 6 7 8 9 10Runs of code

0

50

100

150

200

250

300

350

400

450

()





1518

1520

14 1518 19

1519

5559

5560

5651

54 54 52 53

Num

ber o

f clu

sterin

g pr

oces

ses

1 2 3 4 5 6 7 8 9 10Runs of code

k-meansMk-means

0

10

20

30

40

50

60

70







9081080 1089

2490

2012

1039 1020

2251

1512

1013

361 344 390 326 361 411 391 394 370 385


6 7 8 9 10

Roun

ds o

f com

mun

icat

ion

k-meansMk-means

0

500

1000

1500

2000

2500

3000


Mk-means

Ener

gy (J

)

150100500

Rounds

2

19

18

17

16

15

14

13

12

11

1






k-means

Rounds1009080706050403020100

0

02

04

06

08

1

12

14

16

18

2

Ener

gy (J

)


60

122

219

335358

513

LEAC

H

HEE

D

LEAC

H-C

SECA

0

100

200

300

400

500

600

Roun

ds o

f com

mun

icat

ion

Mk

-mea

ns

k-m

eans





150 161 188255

390 455530 566

1441

LEAC

H

LEAC

H-E

NCA

CM

HEE

D

LEAC

H-C

PEG

ASI

S

SECA

-M

ECRA

Mk

-mea

ns

0

200

400

600

800

1000

1200

1400

1600

Roun

ds o

f com

mun

icat

ion


375 382 405614

968 997 1089 1195

4054

LEAC

H

LEAC

H-E

NCA

CM

HEE

D

LEAC

H-C

PEG

ASI

S

SECA

-M

ECRA

Mk

-mea

ns

0500

10001500200025003000350040004500

Roun

ds o

f com

mun

icat

ion




0 200 400 600 800 1000 1200Rounds

Mk-meansECRASECA-M

k-meansHEEDLEACH

0

05

1

15

2

25

Ener

gy (J

)



6 Conclusion




References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Time




Slot for cluster 3
















































Algorithm 1





3172

43473937

4711

3791

4603 4444

37734162 4072

361 344 390 326 361 411 391 370 385 394

1 2 3 4 5 6 7 8 9 10Runs of code

k-meansMk-means

0500

100015002000250030003500400045005000

Roun

ds





116

136

178

93

165

137

171

61

188

110

1 2 3 4 5 6 7 8 9 10

Incr

ease

()

Runs of code

0

20

40

60

80

100

120

140

160

180

200


2338

3559

2829

4073

28443084 3281

2864 2989 2945

1 2 3 4 5 6 7 8 9 10Runs of code

0

50

100

150

200

250

300

350

400

450

()





1518

1520

14 1518 19

1519

5559

5560

5651

54 54 52 53

Num

ber o

f clu

sterin

g pr

oces

ses

1 2 3 4 5 6 7 8 9 10Runs of code

k-meansMk-means

0

10

20

30

40

50

60

70







9081080 1089

2490

2012

1039 1020

2251

1512

1013

361 344 390 326 361 411 391 394 370 385


6 7 8 9 10

Roun

ds o

f com

mun

icat

ion

k-meansMk-means

0

500

1000

1500

2000

2500

3000


Mk-means

Ener

gy (J

)

150100500

Rounds

2

19

18

17

16

15

14

13

12

11

1






k-means

Rounds1009080706050403020100

0

02

04

06

08

1

12

14

16

18

2

Ener

gy (J

)


60

122

219

335358

513

LEAC

H

HEE

D

LEAC

H-C

SECA

0

100

200

300

400

500

600

Roun

ds o

f com

mun

icat

ion

Mk

-mea

ns

k-m

eans





150 161 188255

390 455530 566

1441

LEAC

H

LEAC

H-E

NCA

CM

HEE

D

LEAC

H-C

PEG

ASI

S

SECA

-M

ECRA

Mk

-mea

ns

0

200

400

600

800

1000

1200

1400

1600

Roun

ds o

f com

mun

icat

ion


375 382 405614

968 997 1089 1195

4054

LEAC

H

LEAC

H-E

NCA

CM

HEE

D

LEAC

H-C

PEG

ASI

S

SECA

-M

ECRA

Mk

-mea

ns

0500

10001500200025003000350040004500

Roun

ds o

f com

mun

icat

ion




0 200 400 600 800 1000 1200Rounds

Mk-meansECRASECA-M

k-meansHEEDLEACH

0

05

1

15

2

25

Ener

gy (J

)



6 Conclusion




References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation







































Algorithm 1





3172

43473937

4711

3791

4603 4444

37734162 4072

361 344 390 326 361 411 391 370 385 394

1 2 3 4 5 6 7 8 9 10Runs of code

k-meansMk-means

0500

100015002000250030003500400045005000

Roun

ds





116

136

178

93

165

137

171

61

188

110

1 2 3 4 5 6 7 8 9 10

Incr

ease

()

Runs of code

0

20

40

60

80

100

120

140

160

180

200


2338

3559

2829

4073

28443084 3281

2864 2989 2945

1 2 3 4 5 6 7 8 9 10Runs of code

0

50

100

150

200

250

300

350

400

450

()





1518

1520

14 1518 19

1519

5559

5560

5651

54 54 52 53

Num

ber o

f clu

sterin

g pr

oces

ses

1 2 3 4 5 6 7 8 9 10Runs of code

k-meansMk-means

0

10

20

30

40

50

60

70







9081080 1089

2490

2012

1039 1020

2251

1512

1013

361 344 390 326 361 411 391 394 370 385


6 7 8 9 10

Roun

ds o

f com

mun

icat

ion

k-meansMk-means

0

500

1000

1500

2000

2500

3000


Mk-means

Ener

gy (J

)

150100500

Rounds

2

19

18

17

16

15

14

13

12

11

1






k-means

Rounds1009080706050403020100

0

02

04

06

08

1

12

14

16

18

2

Ener

gy (J

)


60

122

219

335358

513

LEAC

H

HEE

D

LEAC

H-C

SECA

0

100

200

300

400

500

600

Roun

ds o

f com

mun

icat

ion

Mk

-mea

ns

k-m

eans





150 161 188255

390 455530 566

1441

LEAC

H

LEAC

H-E

NCA

CM

HEE

D

LEAC

H-C

PEG

ASI

S

SECA

-M

ECRA

Mk

-mea

ns

0

200

400

600

800

1000

1200

1400

1600

Roun

ds o

f com

mun

icat

ion


375 382 405614

968 997 1089 1195

4054

LEAC

H

LEAC

H-E

NCA

CM

HEE

D

LEAC

H-C

PEG

ASI

S

SECA

-M

ECRA

Mk

-mea

ns

0500

10001500200025003000350040004500

Roun

ds o

f com

mun

icat

ion




0 200 400 600 800 1000 1200Rounds

Mk-meansECRASECA-M

k-meansHEEDLEACH

0

05

1

15

2

25

Ener

gy (J

)



6 Conclusion




References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



















Algorithm 1





3172

43473937

4711

3791

4603 4444

37734162 4072

361 344 390 326 361 411 391 370 385 394

1 2 3 4 5 6 7 8 9 10Runs of code

k-meansMk-means

0500

100015002000250030003500400045005000

Roun

ds





116

136

178

93

165

137

171

61

188

110

1 2 3 4 5 6 7 8 9 10

Incr

ease

()

Runs of code

0

20

40

60

80

100

120

140

160

180

200


2338

3559

2829

4073

28443084 3281

2864 2989 2945

1 2 3 4 5 6 7 8 9 10Runs of code

0

50

100

150

200

250

300

350

400

450

()





1518

1520

14 1518 19

1519

5559

5560

5651

54 54 52 53

Num

ber o

f clu

sterin

g pr

oces

ses

1 2 3 4 5 6 7 8 9 10Runs of code

k-meansMk-means

0

10

20

30

40

50

60

70







9081080 1089

2490

2012

1039 1020

2251

1512

1013

361 344 390 326 361 411 391 394 370 385


6 7 8 9 10

Roun

ds o

f com

mun

icat

ion

k-meansMk-means

0

500

1000

1500

2000

2500

3000


Mk-means

Ener

gy (J

)

150100500

Rounds

2

19

18

17

16

15

14

13

12

11

1






k-means

Rounds1009080706050403020100

0

02

04

06

08

1

12

14

16

18

2

Ener

gy (J

)


60

122

219

335358

513

LEAC

H

HEE

D

LEAC

H-C

SECA

0

100

200

300

400

500

600

Roun

ds o

f com

mun

icat

ion

Mk

-mea

ns

k-m

eans





150 161 188255

390 455530 566

1441

LEAC

H

LEAC

H-E

NCA

CM

HEE

D

LEAC

H-C

PEG

ASI

S

SECA

-M

ECRA

Mk

-mea

ns

0

200

400

600

800

1000

1200

1400

1600

Roun

ds o

f com

mun

icat

ion


375 382 405614

968 997 1089 1195

4054

LEAC

H

LEAC

H-E

NCA

CM

HEE

D

LEAC

H-C

PEG

ASI

S

SECA

-M

ECRA

Mk

-mea

ns

0500

10001500200025003000350040004500

Roun

ds o

f com

mun

icat

ion




0 200 400 600 800 1000 1200Rounds

Mk-meansECRASECA-M

k-meansHEEDLEACH

0

05

1

15

2

25

Ener

gy (J

)



6 Conclusion




References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










116

136

178

93

165

137

171

61

188

110

1 2 3 4 5 6 7 8 9 10

Incr

ease

()

Runs of code

0

20

40

60

80

100

120

140

160

180

200


2338

3559

2829

4073

28443084 3281

2864 2989 2945

1 2 3 4 5 6 7 8 9 10Runs of code

0

50

100

150

200

250

300

350

400

450

()





1518

1520

14 1518 19

1519

5559

5560

5651

54 54 52 53

Num

ber o

f clu

sterin

g pr

oces

ses

1 2 3 4 5 6 7 8 9 10Runs of code

k-meansMk-means

0

10

20

30

40

50

60

70







9081080 1089

2490

2012

1039 1020

2251

1512

1013

361 344 390 326 361 411 391 394 370 385


6 7 8 9 10

Roun

ds o

f com

mun

icat

ion

k-meansMk-means

0

500

1000

1500

2000

2500

3000


Mk-means

Ener

gy (J

)

150100500

Rounds

2

19

18

17

16

15

14

13

12

11

1






k-means

Rounds1009080706050403020100

0

02

04

06

08

1

12

14

16

18

2

Ener

gy (J

)


60

122

219

335358

513

LEAC

H

HEE

D

LEAC

H-C

SECA

0

100

200

300

400

500

600

Roun

ds o

f com

mun

icat

ion

Mk

-mea

ns

k-m

eans





150 161 188255

390 455530 566

1441

LEAC

H

LEAC

H-E

NCA

CM

HEE

D

LEAC

H-C

PEG

ASI

S

SECA

-M

ECRA

Mk

-mea

ns

0

200

400

600

800

1000

1200

1400

1600

Roun

ds o

f com

mun

icat

ion


375 382 405614

968 997 1089 1195

4054

LEAC

H

LEAC

H-E

NCA

CM

HEE

D

LEAC

H-C

PEG

ASI

S

SECA

-M

ECRA

Mk

-mea

ns

0500

10001500200025003000350040004500

Roun

ds o

f com

mun

icat

ion




0 200 400 600 800 1000 1200Rounds

Mk-meansECRASECA-M

k-meansHEEDLEACH

0

05

1

15

2

25

Ener

gy (J

)



6 Conclusion




References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










9081080 1089

2490

2012

1039 1020

2251

1512

1013

361 344 390 326 361 411 391 394 370 385


6 7 8 9 10

Roun

ds o

f com

mun

icat

ion

k-meansMk-means

0

500

1000

1500

2000

2500

3000


Mk-means

Ener

gy (J

)

150100500

Rounds

2

19

18

17

16

15

14

13

12

11

1






k-means

Rounds1009080706050403020100

0

02

04

06

08

1

12

14

16

18

2

Ener

gy (J

)


60

122

219

335358

513

LEAC

H

HEE

D

LEAC

H-C

SECA

0

100

200

300

400

500

600

Roun

ds o

f com

mun

icat

ion

Mk

-mea

ns

k-m

eans





150 161 188255

390 455530 566

1441

LEAC

H

LEAC

H-E

NCA

CM

HEE

D

LEAC

H-C

PEG

ASI

S

SECA

-M

ECRA

Mk

-mea

ns

0

200

400

600

800

1000

1200

1400

1600

Roun

ds o

f com

mun

icat

ion


375 382 405614

968 997 1089 1195

4054

LEAC

H

LEAC

H-E

NCA

CM

HEE

D

LEAC

H-C

PEG

ASI

S

SECA

-M

ECRA

Mk

-mea

ns

0500

10001500200025003000350040004500

Roun

ds o

f com

mun

icat

ion




0 200 400 600 800 1000 1200Rounds

Mk-meansECRASECA-M

k-meansHEEDLEACH

0

05

1

15

2

25

Ener

gy (J

)



6 Conclusion




References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










150 161 188255

390 455530 566

1441

LEAC

H

LEAC

H-E

NCA

CM

HEE

D

LEAC

H-C

PEG

ASI

S

SECA

-M

ECRA

Mk

-mea

ns

0

200

400

600

800

1000

1200

1400

1600

Roun

ds o

f com

mun

icat

ion


375 382 405614

968 997 1089 1195

4054

LEAC

H

LEAC

H-E

NCA

CM

HEE

D

LEAC

H-C

PEG

ASI

S

SECA

-M

ECRA

Mk

-mea

ns

0500

10001500200025003000350040004500

Roun

ds o

f com

mun

icat

ion




0 200 400 600 800 1000 1200Rounds

Mk-meansECRASECA-M

k-meansHEEDLEACH

0

05

1

15

2

25

Ener

gy (J

)



6 Conclusion




References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article Balanced Cluster Head Selection Based on …downloads.hindawi.com/journals/ijdsn/2016/5040475.pdf · 2016-03-10 · Research Article Balanced Cluster Head Selection