Upload
gabe
View
36
Download
0
Embed Size (px)
DESCRIPTION
A configuration method for structured P2P overlay network considering delay variations. Tomoya KITANI (Shizuoka Univ. 、 Japan) Yoshitaka NAKAMURA (NAIST, Japan). Overview. A Novel Space Filling Curve efficiently lets a 2D space coordinate be converted into a 1D space - PowerPoint PPT Presentation
Citation preview
A configuration method for structured P2P overlay network
considering delay variationsTomoya KITANI (Shizuoka Univ. 、 Japan)
Yoshitaka NAKAMURA (NAIST, Japan)
Overview
8/20/20092
A Novel Space Filling Curve efficiently lets a
2D space coordinate be converted into a 1D space
easily gives each node ID from the space coordinate and the link delay between the nodes
Backgrounds
8/20/20093
Realization of location-aware service by the spread of mobile Internet environment Providing the service that considered the location
information of the node
P2P overlay network based on location information Advertisement for the specific area is possible
Range specified information search
Related work
8/20/20094
LL-net Structured P2P overlay network where the
area on the map is hierarchically divided into 4 sub areas, and in each hierarchy the overlay links should be the different length
Dynamic construction of overlay network by join/leave of mobile terminals
Related work
8/20/20095
SkipGraph Performance of LL-net turns worse by deflection of
nodes LL-net constructs quad-tree and search over the tree Depth of the tree is biased because nodes are
distributed following power law in reality
Efficiency of the search can be kept O(log N) at any time by usingSkipGraph into LL-net
SkipGraph uses ID mapping 2D information to 1D
Mapping 2D->1D Space Filling Curve
Space filling curve
8/20/20096
known as technique to map information of a multi-dimensional space such as location information onto the one-dimensional(1D) space such as ID
One-dimensional ID Can use the distributed resource management
technique of P2P DHT, SkipGraph, etc.
Conventional Space Filling Curves Lebesgue curve (Z-ordering) Hilbert curve Sierpinski curve
Lebesgue Curve ( Z-ordering )
8/20/20097
Divide into 4 clusters and connect nodes in the shape of Z
Physical link length between clusters is long
The nodes that are near on 2D space may not become near on 1D space either
Lebesgue is used well practically because conversion from latitude and longitude is easy
Node labeling using location information
8/20/20098
Geographical location information ((x,y)) of 2D space is converted into 1D x = (x1 x2 x3 ... xH) y = (y1 y2 y3 ... yH) p = (x1 y1 x2 y2 x3 y3 ... xH yH)
Go around in order ofassuming p as a binarynumber
-> Lebesgue Curve(Z-ordering )
0000
0010
1000
1010
0001
0011
1001
1011
0100
0110
1100
1110
0101
0111
1101
1111
x00 01 10 11
00
01y
10
11
Hilbert Curve
8/20/20099
All nodes are connected with a link of length 1
Neighbor nodes on the 2D space are relatively near also on 1D space
It is complex to calculate the position in 1D space from latitude and longitude
Advantage of space filling curve
8/20/200910
Geographically near nodes are close in 1D-ID Information search that specifies the range is
efficiently executable when the information related to location information
Divide into 5 ranges
and search
Divide into 3 ranges
and search
New space filling curve
8/20/200911
Purpose Convertible from latitude and longitude easily as
the Lebesgue curve Convertible geographically near node into near ID
Introduction of label and connection relationship of Hierarchical Chordal Ring Network Hamming distance between the neighbor nodes’
ID can be 1
Hierarchical Chordal Ring Network20)
8/20/200912
Topology where number of average hops and network diameter are assumed O(log N) based on ring type network HCRN has the ring type
structure and the tree structure
HCRN is originally designed so that numberof necessary wave length may become O(log N) on ring type WDM network
ID labeling of HCRN
8/20/200913
0000
0010
1000
1010
0001
0011
1001
1011
0100
0110
1100
1110
0101
0111
1101
1111
x00 01 10 11
00
01y
10
11
00
01
10
11
Correspondence to dynamic join/leave of nodes
8/20/200914
Hierarchical number of each segmented domain depends on the number of participating nodes
Space filling curve that covers all nodes that belong to all hierarchies is proposed
In Lebesgue, it is possible to correspond by enhancing to arrange nodes of a higher hierarchy in the oblique side of Z character
Generation processes of HCRN from latitude & longitude
8/20/200915
Generate by the following conversion processes1. (x,y) : latitude & longitude of the node of the k th hierarchy2. To adjust Hamming distance of the label between the
neighbor nodes to 1, Each even number bits of x, y
are reversed and
p = (x1 y1 x2 y2 x3 y3 ... xk yk)= (p1... p2k) is obtained
3. Sequence number seqp is obtained by rightexpression (H is themaximum number ofhierarchy)
4. Nodes are connected inorder of seqp
New space filling curve using HCRN
8/20/200916
Label lp of HCRN is obtained from p with the following conversions
Nodes with Hamming distance 1 are connected
This curve is closed space filling curve looks like Hilbert and is connected hierarchically
)1( ppl p
Evaluation of proposed curve
8/20/200917
Object of comparison Proposed curve(2D-HCRN) Lebesgue curve Lebesgue enhanced to multi
hierarchies(2D-Lebesgue) Lowest hierarchy of proposed
curve Hilbert curve
Evaluation item Distance on 1D-ID with the neighborhood nodes on 2D
by Index Range. Delay to need to go around all nodes by simulation
Index Range19)
8/20/200918
To evaluate how far each two nodes physically in 4 neighborhoods on the filling curves Logarithmic average distance on 1D-ID of
geographically 4 neighborhoods seq(i) : Sequence number on 1D-ID of node i pos(i) : Position (x,y) on 2D-plane of node i
Index Range of each space filling curve
8/20/200919
Sm
alle
r is
bett
er
Simulation environment
8/20/200920
10-10,000 nodes participate into the network sequentially
Nodes join according to the following algorithm1. The node with latitude & longitude p = (x1 y1 x2 y2 ... xH yH) = (p1 p2 ... p2H)
joins2. i = 23. If the node with the label of
p’ = (p1... pi) does not exist yet, p’ isassumed to be a label that shows thelocation information of the node
4. If there is p‘ , i = i + 2 and go to 3.
1. Position p of the participation node is decided by a random number according to "randomdistribution" and "Zipf distribution"
Average physical distance between neighbor nodes in ID (Randomly distributed)
8/20/200921
Average physical distance between neighbor nodes in ID (Distributed following Zipf law)
8/20/200922
Square average of physical distance between neighbor nodes in ID (Randomly distributed)
8/20/200923
Square average of physical distance between neighbor nodes in ID (Distributed following Zipf law)
8/20/200924
Conclusions
8/20/200925
We proposed the new space filling curve for small delay structured P2P overlay network Geographical round distance is small and
conversion is comparatively easy More suitable for hierarchical-spread nodes than
the conventional curves
Future work Performance evaluation of the proposed space
filling curve in the real network environment especially in node distribution with bias
Reexamination of the routing entry of each node to improve the performance