Abstract.
In this paper we give three subcubic 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(log 2 n) time with \(O(n^\mu/\sqrt{\log n})\) 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 nonnegative general costs (real numbers) in O(log 2 n) time with o(n 3 ) subcubic cost. Previously this cost was greater than O(n 3 ) . 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 to O(M 1/3 n (6+ω)/3 (log n) 2/3 (log log n) 1/3 ) in the APSD problem, where ω = 2.376 .
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Received October 15, 1995; revised June 21, 1996.
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Takaoka, T. Subcubic Cost Algorithms for the All Pairs Shortest Path Problem . Algorithmica 20, 309–318 (1998). https://doi.org/10.1007/PL00009198
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DOI: https://doi.org/10.1007/PL00009198