TY - GEN

T1 - (1 + ϵ)-Approximate f-sensitive distance oracles

AU - Chechik, Shiri

AU - Cohen, Sarel

AU - Fiat, Amos

AU - Kaplan, Haim

N1 - Publisher Copyright:
Copyright © by SIAM.

PY - 2017

Y1 - 2017

N2 - An f-Sensitive Distance Oracle with stretch α 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 n F (the graph obtained from G by discarding all edges in F). Moreover, d is at most α times the length of the shortest path between s and t in G n F. The oracle can also construct a path between s and t in Gn 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 f = o( log n log log n ) and a fixed ϵ > 0 our oracle answers queries (F; s; t) in time e O(1) with (1 + ϵ) stretch using a data structure of size n2+o(1). For comparison, the naive alternative requires mfn2 space for sublinear query time.

AB - An f-Sensitive Distance Oracle with stretch α 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 n F (the graph obtained from G by discarding all edges in F). Moreover, d is at most α times the length of the shortest path between s and t in G n F. The oracle can also construct a path between s and t in Gn 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 f = o( log n log log n ) and a fixed ϵ > 0 our oracle answers queries (F; s; t) in time e O(1) with (1 + ϵ) stretch using a data structure of size n2+o(1). For comparison, the naive alternative requires mfn2 space for sublinear query time.

UR - http://www.scopus.com/inward/record.url?scp=85016200777&partnerID=8YFLogxK

U2 - 10.1137/1.9781611974782.96

DO - 10.1137/1.9781611974782.96

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AN - SCOPUS:85016200777

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1479

EP - 1496

BT - 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017

A2 - Klein, Philip N.

PB - Association for Computing Machinery

T2 - 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017

Y2 - 16 January 2017 through 19 January 2017

ER -