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CORR
2012
Springer

Faster Approximate Distance Queries and Compact Routing in Sparse Graphs

8 years 5 months ago
Faster Approximate Distance Queries and Compact Routing in Sparse Graphs
A distance oracle is a compact representation of the shortest distance matrix of a graph. It can be queried to retrieve approximate distances and corresponding paths between any pair of vertices. A lower bound, due to Thorup and Zwick, shows that a distance oracle that returns paths of worst-case stretch (2k − 1) must require space Ω(n1+1/k ) for graphs over n nodes. The hard cases that enforce this lower bound are, however, rather dense graphs with average degree Ω(n1/k ). We present distance oracles that, for sparse graphs, substantially break the lower bound barrier at the expense of higher query time. For any 1 ≤ α ≤ n, our distance oracles can return stretch 2 paths using O(m + n2 /α) space and stretch 3 paths using O(m + n2 /α2 ) space, at the expense of O(αm/n) query time. By setting appropriate values of α, we get the first distance oracles that have size linear in the size of the graph, and return constant stretch paths in non-trivial query time. The query tim...
Rachit Agarwal, Brighten Godfrey, Sariel Har-Peled
Added 20 Apr 2012
Updated 20 Apr 2012
Type Journal
Year 2012
Where CORR
Authors Rachit Agarwal, Brighten Godfrey, Sariel Har-Peled
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