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Efficient Broadcasting and Gathering in Wireless Ad-Hoc Networks

Melih Onus (ASU)Kishore Kothapalli (JHU)Andrea Richa (ASU)Christian Scheideler (JHU)

2005 International Symposium on Parallel Architectures, Algorithms and Networks, Las Vegas Nevada

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Ad-Hoc Networks

Mobile devices communicating via radio Network without centralized control Broadcasting: Sending a packet from a source

node to all nodes in the network Gathering: Sending one packet from a subset of

nodes to a single sink node in the network

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Our Results

Near optimal algorithms for broadcasting and information gathering (time and work)

A realistic wireless communication model which takes into account– Different transmission & interference ranges– Non-uniformity of signal propagation of real antennas– Physical carrier sensing

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Communication Models

Unit Disk Graph (UDG) Disk shaped transmission area

uR

vw

Packet Radio Network (PRN) Transmission Range = Interference Rangev

u

w

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Communication model

u

v

w

rt

ri

For a given transmission range rt, transmission area of v is

{ uV | c(v,u) rt }

Transmission range, interference area via cost function c

For given interference range ri, interference area of v is

{ uV | c(v,u) ri }

Cost Function:

c(u,v) [(1- )d(u,v), (1+ )d(u,v)]

d(u,v) is Euclidean distance [0,1), depends on the environment

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Communication model (cont.)

u

v

w

rt

ri

If c(v,u) ≤rt then v is guaranteed to receive the message from u provided no other node w with c(v, w) ≤ ri also transmits at the same time.

rt: Transmission rangeri: Interference range

If c(v,w) ≤ ri, node w can cause interference at node v.

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Physical Carrier Sensing

These ranges grow monotonically in both the sensing threshold T and the transmission power.

ursi(T)

v

w rst(T): Carrier sense transmission (CST) range

rst(T)

rsi(T): Carrier sense interference (CSI) range

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Constant density spanner

Constant density spanner: Given a graph G find a sparse subgraph G’ of G such that distance between any two nodes in G’ is less than a constant factor of original distance.

Active node

Inactive node

Gateway node

Gateway edge

Other edges

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Constant density spanner (cont.)

Active nodes form a maximal independent setGateway nodes connect active nodes which are within 2 or 3 hops from each other

Active node

Inactive node

Gateway node

Gateway edge

Other edges

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Motivation

Previously proposed broadcasting and gathering algorithms will not work for the communication model that we have considered.

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s( )(( ))

Isolated Broadcasting

Active node

Inactive node

Gateway node

Gateway edge

Other edges

Firstly, node s sends out the broadcast message.

((( ))) vu

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message

CTS

RTS

Isolated Broadcasting (cont.)

If u is a gateway node and has already received the message, it sends out an RTS signal with probability p.

If v is an active node or a gateway node and v has not received the broadcast message yet, then v checks if it correctly received an RTS signal. If so, v sends out a CTS signal.

If v is a gateway node and sent out a RTS signal, then v checks if it received a CTS signal. If so, v sends out the broadcast message.

svu

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Isolated Broadcasting (cont.)

Active node

Inactive node

Gateway node

Gateway edge

Other edges

sv

u

(( ))((( )))( )

If node v:– is an active node

– received the broadcast message in the previous round

– it is the first time it received the broadcast message Then, it sends out the broadcast message.

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Our Results

D(s): diameter with respect to s W(s): minimum work for broadcast

The broadcast algorithm needs O(D(s)+log n) rounds, with high probability, to deliver the broadcast messages to all nodes.

The broadcast algorithm needs O(W(s)) work Extendable to multiple broadcasts

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Information Gathering

Stage I: Building Gathering Tree T(s) Stage II: Gathering on Tree T(s)

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Building Gathering Tree T(s)

We select a shortest path tree rooted at s on the spanner graph by running a modified Bellman-Ford type algorithm that takes into account message interference.

In order to show that this RTS/CTS scheme works efficiently, it is crucial to note that the spanner is of constant density: Hence a constant number of RTS/CTS handshakes are enough to guarantee the successful delivery of a message w.h.p..

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RTSroute m.

Building Gathering Tree T(s) (cont.)

CTSs

vu

Firstly, node s sends out the route message.

<0> <1>(( ))((( )))( )

If the shortest path estimate d'(s,u) is not infinite and u needs to broadcast the latest update on d’(s,u), then u sends a RTS signal with probability p

If v received an RTS signal then v sends a CTS signal.

If u received a CTS signal, u sends out the route message.

<2>

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Building Gathering Tree T(s) (cont.)

svu

<0> <1>

Each node u has a label which is the shortest path distance to sink node.

<2>

<3>

<3><4>

<4>

<5>

<5>

<6>

<6> <7>

Each node u has a parent node which is the node that node u received the route message

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I-RTS

Gathering on Tree T(s) (Inactive Nodes)

Active node

Inactive node

Gateway node

Gateway edge

Other edges

If w is inactive and has a packet to send and w is awake then w sends a I-RTS signal to its parent with a probability 1/2.

s

w

Inactive nodes have a state {asleep, awake}

v

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Gathering on Tree T(s) (Inactive Nodes)

Active node

Inactive node

Gateway node

Gateway edge

Other edges

s

w

v

If v is active; v receives an I-RTS signal, send an I-CTS signal v senses a busy channel, send a collision message v senses a free channel, send a free message

I-RTS

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Gathering on Tree T(s) (Inactive Nodes)

Active node

Inactive node

Gateway node

Gateway edge

Other edges

s

w

v

If w is inactive; w receives an I-CTS signal, send the packet w receives a collision message, become asleep with p=1/2 w receives a free message, become awake

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Gathering on Tree T(s) (Active Nodes)

Active node

Inactive node

Gateway node

Gateway edge

Other edges

If v is active and has a message to send, then v sends the message to its parent.

sv

u

message

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RTS

Gathering on Tree T(s) (Gateway Nodes)

Active node

Inactive node

Gateway node

Gateway edge

Other edges

If u is a gateway node and has a non-empty queue then u sends an RTS message containing the id of its parent with probability p.

If u receives a CTS message from its parent, then u sends the message to its parent.

If an active node receives an RTS message containing its id, it sends a CTS message.

sv

u

CTS

message

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Our Results

: maximum density of inactive nodes m: number of messages W’(s): the optimal work

A gathering tree T(s) with sink node s, the information gathering algorithm presented above needs O(m+(logn)(log)+D(s)+logn) time steps w.h.p..

Once a stable gathering tree has been constructed, the gathering protocol described above needs O(W’(s)) work

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Conclusions and Future work Algorithms for broadcasting and information

gathering on a realistic model for wireless communication

Node mobility and node faults Anycasting and multicasting