The Space-Stretch-Time Tradeoff in Distance Oracles

We present distance oracles for weighted undirected graphs that return distances of stretch 2 and less. For the realistic case of sparse graphs, our distance oracle exhibit the 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/α) and returns stretch (1+2/(t+1)) distances in time O((α∆)), where ∆ = 2m/n is the average degree of the graph. The query time can be further reduced to O((α+∆)) at the expense of a small additive stretch. Consider, for example, the realistic case of graphs with m = Õ(n) edges and fix the query time to be Õ(n). Our distance oracles, then, return stretch 2 distances using space O(n) and stretch 5/3 distances using space O(n). University of Illinois, Urbana, IL 61801. Email: [email protected].