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Improved Distance Sensitivity Oracles via Tree Partitioning

  • Ran Duan
  • Tianyi Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10389)

Abstract

We introduce an improved structure of distance sensitivity oracle (DSO). The task is to pre-process a non-negatively weighted graph so that a data structure can quickly answer replacement path length for every triple of source, terminal and failed vertex. The previous best algorithm [Bernstein and Karger, 2009] constructs in time (\(\tilde{O}(\cdot )\) suppresses poly-logarithmic factors.) \(\tilde{O}(mn)\) a distance sensitivity oracle of size \(O(n^2\log n)\) that processes queries in O(1) time. As an improvement, our oracle takes up \(O(n^2)\) space, while preserving O(1) query efficiency and \(\tilde{O}(mn)\) preprocessing time. One should notice that space complexity and query time of our novel data structure are asymptotically optimal.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Tsinghua UniversityBeijingChina

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