The space-stretch-time tradeoff in distance oracles

Abstract

We present new distance oracles for computing distances of stretch less than 2 on general weighted undirected graphs. For the realistic case of sparse graphs and for any integer k, the new oracles return paths of stretch 1+1/k and exhibit a smooth three-way tradeoff of S ×T 1/k =O(n 2) between space S, stretch and query time T. This significantly improves the state-of-the-art for each point in the space-stretch-time tradeoff space, and matches the known space-time curve for stretch 2 and larger. We also present new oracles for stretch 1+1/(k+0.5). A particularly interesting case is of stretch 5/3, where improving the query time of our oracles from T to T 1-ε for any ε>0 would lead to the first purely o(mn)-time combinatorial algorithm for Boolean Matrix Multiplication, a longstanding open problem. © 2014 Springer-Verlag Berlin Heidelberg.