1. A configuration method for structured P2P overlay network considering delay variations Tomoya KITANI (Shizuoka Univ. 、 Japan) Yoshitaka NAKAMURA (NAIST, Japan)

2. 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

3. 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

4. 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

5. 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->1DSpace Filling Curve

6. 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

7. 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

8. Node labeling using location information 8/20/20098  Geographical location information ( (x,y) ) of 2D space is converted into 1D  x = (x 1 x 2 x 3... x H )  y = (y 1 y 2 y 3... y H )  p = (x 1 y 1 x 2 y 2 x 3 y 3... x H y H )  Go around in order of assuming p as a binary number -> Lebesgue Curve (Z-ordering ） 00000000001000101000100010101010 00010001001100111001100110111011 01000100011001101100110011101110 01010101011101111101110111111111 x 00 01 10 11 00 01 y 10 11

9. 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

10. 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

11. 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

12. Hierarchical Chordal Ring Network 20) 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 number of necessary wave length may become O(log N) on ring type WDM network

13. ID labeling of HCRN 8/20/200913 00000000001000101000100010101010 00010001001100111001100110111011 01000100011001101100110011101110 01010101011101111101110111111111 x 00 01 10 11 00 01 y 10 11 0 0101 1010 1

14. 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

15. Generation processes of HCRN from latitude & longitude 8/20/200915  Generate by the following conversion processes 1. (x,y) : latitude & longitude of the node of the k th hierarchy 2. To adjust Hamming distance of the label between the neighbor nodes to 1,  Each even number bits of x, y are reversed and p = (x 1 y 1 x 2 y 2 x 3 y 3... x k y k )= (p 1... p 2k ) is obtained 3. Sequence number seq p is obtained by right expression (H is the maximum number of hierarchy) 4. Nodes are connected in order of seq p

16. New space filling curve using HCRN 8/20/200916  Label l p 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

17. 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

18. Index Range 19) 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

19. Index Range of each space filling curve 8/20/200919 Smaller is better

20. Simulation environment 8/20/200920  10-10,000 nodes participate into the network sequentially  Nodes join according to the following algorithm 1. The node with latitude & longitude p = (x 1 y 1 x 2 y 2... x H y H ) = (p 1 p 2... p 2H ) joins 2. i = 2 3. If the node with the label of p’ = (p 1... p i ) does not exist yet, p’ is assumed to be a label that shows the location information of the node 4. If there is p‘, i = i + 2 and go to 3.  Position p of the participation node is decided by a random number according to "random distribution" and "Zipf distribution"

21. Average physical distance between neighbor nodes in ID (Randomly distributed) 8/20/200921

22. Average physical distance between neighbor nodes in ID (Distributed following Zipf law) 8/20/200922

23. Square average of physical distance between neighbor nodes in ID (Randomly distributed) 8/20/200923

24. Square average of physical distance between neighbor nodes in ID (Distributed following Zipf law) 8/20/200924

25. 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