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...

• Type: Journal
• Year: 2012
• Where: CORR
• Authors: Rachit Agarwal, Brighten Godfrey, Sariel Har-Peled
• Keywords: CORR 2012, Dense Graphs, Education, Internet Graph, Unweighted Graphs