Distance Oracles for Stretch Less Than 2 [chapter]

Rachit Agarwal, P. Brighten Godfrey
2013 Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms  
We present distance oracles for weighted undirected graphs that return distances of stretch less than 2. For the realistic case of sparse graphs, our distance oracles exhibit a smooth three-way trade-off between space, stretch and query time -a phenomenon that does not occur in dense graphs. In particular, for any positive integer t and for any 1 ≤ α ≤ n, our distance oracle is of size O(m + n 2 /α) and returns distances of stretch at most (1 + 2 t+1 ) in time O((αµ) t ), where µ = 2m/n is the
more » ... verage degree of the graph. The query time can be further reduced to O((α + µ) t ) at the expense of a small additive stretch.
doi:10.1137/1.9781611973105.38 dblp:conf/soda/AgarwalG13 fatcat:rtskv7wtfraann2cwararo5g7e