Multi-level Proximity Routing and

its applications for Networking

Tomer Tankel

Dept. of Electrical Eng. – Systems

Problem and Applications

Problems:Using Measurement for distance estimation Routing in fixed and Ad Hoc networksNavigation in Traffic NetworksApplications:Closest mirror selection

Given a set of servers, si 1≤i≤K, and a client, c, find a server sj, s.t., i 1≤i≤K d(sj,c)≤ αd(si,c)+β

Content Distribution in P2P networksReal-Time Vehicle Routing Server

Distance Estimation/Routing Issues

• Scalability– Complexity (Memory, CPU)– Measurement Approximated Input– Dissemination

• Need Accurate & Fast Query Algorithm!

Multi-level Proximity Routing (MPR)

• Limited routing scope (2-neighborhood)

• Neglect a node if its neighbors selected.

• Neglect longer paths between nodes.

Multi-level Proximity Routing

1

2

3

4

SiblingEdge

Each cluster head i which is not selected iteratively select neighbors j1,j2 …jk with maximum select score until

Here <1 is the aggregation factor. Increasing it yields more optimal but denser

MPR, with larger memory and run time complexities.

Select Stage

• l-level parents path types

where p1,2 are parents of child u1,2.

• Remove edge i→j if not shorter than

Interpolate Stage

MPR Experiments

Graph Nodes Arcs/ Edges

Basic MPR CPU*

Build sec Query ms

DIMES IP Delay

w16/08138721 602970

(directed)47.7 0.15

DIMACS

9’th Euro-Road

18010173 42188664

(directed)1681.3 0.42

Simulate Ad-Hoc

1281966 8554957

(undirected)688.1 1.9

DIMES IP Delay

0 0.03 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Basic-MPR AccuracyDIMES IP Delay week 31/2007

Relative Delay Error

CC

DF

Full ScanSpeedup Gap=8

Max 2.26(102.9ms)Median 0.029

Max 5.35(103.3ms)Median 0.048

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.410

-4

10-3

10-2

10-1

100

p-MPR Accuracy

DIMES IP Delay week 31/2007 p=0.7

Relative Delay Error

CC

DF

Full ScanSpeedup Gap=8

Max 0.307(7.08ms)

Max 1.18(31.9ms)

0 0.02 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Basic-MPR AccuracyDIMACS 9'th Europe Road Network

Relative Time Error

CC

DF

Full ScanSpeedup Gap=8

Max 7.16(25h:45m)Median 0.05Max 0.88(3h:20m)

Median 0.017

Euro-Road Network

Conclusion

• MPR is a scalable approach to– Routing– Location– Distance Estimation– Sensor and Ad Hoc networks– Multicast

• Multi-level for high complexity graph problems– Qos Routing– Embedding