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Sub-cubic cost algorithms for the all pairs shortest path problem

  • Tadao Takaoka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1017)

Abstract

In this paper we give three sub-cubic cost algorithms for the all pairs shortest distance (APSD) and path (APSP) problems. The first is a parallel algorithm that solves the APSD problem for a directed graph with unit edge costs in O(log2n) time with \(O({{n^\mu } \mathord{\left/{\vphantom {{n^\mu } {\sqrt {\log n} }}} \right.\kern-\nulldelimiterspace} {\sqrt {\log n} }})\) processors where Μ=2.688 on an EREW-PRAM. The second parallel algorithm solves the APSP, and consequently APSD, problem for a directed graph with non-negative general costs (real numbers) in O(log2n) time with o(n3) subcubic cost. Previously this cost was greater than O(n3). Finally we improve with respect to M the complexity O((Mn)μ) of a sequential algorithm for a graph with edge costs up to M into O(M1/3n6+1/3/3(log n)2/3(log log n)1/3) in the APSD problem.

Keywords

Short Path Directed Graph Matrix Multiplication Parallel Algorithm Short Path Problem 
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 1995

Authors and Affiliations

  • Tadao Takaoka
    • 1
  1. 1.Department of Computer ScienceIbaraki UniversityIbarakiJapan

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