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The Space-Stretch-Time Tradeoff in Distance Oracles

  • Rachit Agarwal
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8737)

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.

Keywords

Short Path Hash Table Query Time Sparse Graph Query Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Rachit Agarwal
    • 1
  1. 1.University of California at BerkeleyUSA

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