(1 + ∊)-Approximate f-Sensitive Distance Oracles

Shiri Chechik, Sarel Cohen, Amos Fiat, Haim Kaplan

Abstract: An f-Sensitive Distance Oracle with stretch a preprocesses a graph G(V, E) and produces a small data structure that is used to answer subsequent queries. A query is a triple consisting of a set F ⊂ E of at most f edges, and vertices s and t. The oracle answers a query (F,s.,t) by returning a value d which is equal to the length of some path between s and t in the graph G\F (the graph obtained from G by discarding all edges in F). Moreover, d is at most a times the length of the shortest path between s and t in G \ F. The oracle can also construct a path between s and t in G\F of length d. To the best of our knowledge we give the first nontrivial f-sensitive distance oracle with fast query time and small stretch capable of handling multiple edge failures. Specifically, for any and a fixed ∊ > 0 our oracle answers queries (F,s,t) in time O(l) with (1 + ∊) stretch using a data structure of size n2+0(1) For comparison, the naive alternative requires mfn2 space for sublinear query time.