Journal ArticleDOI
A compact routing scheme and approximate distance oracle for power-law graphs
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TLDR
This work provides alabeled routing scheme that, after a stretch--5 handshaking step (similar to DNS lookup in TCP/IP), routes messages along stretch--3 paths and obtains the first analytical bound coupled to the parameter of the power-law graph model for a compact routing scheme.Abstract:
Compact routing addresses the tradeoff between table sizes and stretch, which is the worst-case ratio between the length of the path a packet is routed through by the scheme and the length of an actual shortest path from source to destination. We adapt the compact routing scheme by Thorup and Zwick [2001] to optimize it for power-law graphs. We analyze our adapted routing scheme based on the theory of unweighted random power-law graphs with fixed expected degree sequence by Aiello et al. [2000]. Our result is the first analytical bound coupled to the parameter of the power-law graph model for a compact routing scheme.Let n denote the number of nodes in the network. We provide a labeled routing scheme that, after a stretch--5 handshaking step (similar to DNS lookup in TCP/IP), routes messages along stretch--3 paths. We prove that, instead of routing tables with O(n1/2) bits (O suppresses factors logarithmic in n) as in the general scheme by Thorup and Zwick, expected sizes of O(nγ log n) bits are sufficient, and that all the routing tables can be constructed at once in expected time O(n1+γ log n), with γ = τ-22/τ-3 + e, where τ∈(2,3) is the power-law exponent and e 0 (which implies eread more
Citations
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References
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Proceedings Article
Compact Routing Tables for Graphs of Bounded Genus
Cyril Gavoille,Nicolas Hanusse +1 more
TL;DR: For planar graphs on n nodes, the authors showed how to construct in linear time shortest path routing tables that require 8n + o(n) bits per node, and O(log2+ǫ n) bit-operations per node to extract the route, with constant ǫ > 0.
Proceedings ArticleDOI
Reducing Maximum Stretch in Compact Routing
TL;DR: A simple greedy scheme for landmark selection that takes a desired stretch s and a budget L on the number of landmarks as input, and produces a set of at most 0(L logn) landmarks that achieve stretch s, which produces routing tables that use no more than O(logn) more space than the optimum scheme for achieving stretch s with L landmarks.
Book ChapterDOI
Compact Routing Tables for Graphs of Bounded Genus (Extended Abstract)
Cyril Gavoille,Nicolas Hanusse +1 more
TL;DR: This work shows how to construct in linear time shortest path routing tables that require 8n + o(n) bits per node, and O(log2+∈ n) bit-operations per node to extract the route, and generalizes the result for every graph of bounded crossing-edge number.
Proceedings Article
Random graph models for the web graph.
Ravi Kumar,Prabhakar Raghavan,Sridhar Rajagopalan,Dandapani Sivakumar,Andrew Tomkins,Eli Upfal +5 more
Book ChapterDOI
Compact routing for graphs excluding a fixed minor
TL;DR: It is proved an Ω(ne) space lower bound for some constant e > 0.1 holds even for bounded degree triangulations, and is optimal for polynomially weighted planar graphs (e=1/2).