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