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 ArticleDOI
Hyperbolic Embedding and Routing for Dynamic Graphs
Andrej Cvetkovski,Mark Crovella +1 more
TL;DR: A simple but robust generalization of greedy distance routing called Gravity-Pressure (GP) routing is proposed, which always succeeds in finding a route to the destination provided that a path exists, even if a significant fraction of links or nodes is removed subsequent to the embedding.
Proceedings ArticleDOI
A sketch-based distance oracle for web-scale graphs
TL;DR: This work studies the fundamental problem of computing distances between nodes in large graphs such as the web graph and social networks, and moves the time-consuming shortest-path computation offline, and at query time only looks up precomputed values and performs simple and fast computations on these precomputable values.
Proceedings ArticleDOI
Greedy Forwarding in Dynamic Scale-Free Networks Embedded in Hyperbolic Metric Spaces
Proceedings ArticleDOI
Routing in Networks with Low Doubling Dimension
TL;DR: The first name-independent solution for compact routing schemes for networks with low doubling dimension is provided, and a lower bound requiring linear storage for stretch \gt 3 schemes is proved.
Proceedings ArticleDOI
Compact name-independent routing with minimum stretch
TL;DR: Given a weighted undirected network with arbitrary node names, this work presents a compact routing scheme, using a Õ(√n) space routing table at each node, and routing along paths of stretch 3, that is, at most thrice as long as the shortest paths.