On the Exponent of the All Pairs Shortest Path Problem
نویسندگان
چکیده
منابع مشابه
On the Exponent of the All Pairs Shortest Path Problem
The upper bound on the exponent, ω, of matrix multiplication over a ring that was three in 1968 has decreased several times and since 1986 it has been 2.376. On the other hand, the exponent of the algorithms known for the all pairs shortest path problem has stayed at three all these years even for the very special case of directed graphs with uniform edge lengths. In this paper we give an algor...
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The Shoshan-Zwick algorithm solves the all pairs shortest paths problem in undirected graphs with integer edge costs in the range {1, 2, . . . ,M}. It runs in Õ(M · n) time, where n is the number of vertices, M is the largest integer edge cost, and ω < 2.3727 is the exponent of matrix multiplication. It is the fastest known algorithm for this problem. This paper points out the erroneous behavio...
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 1997
ISSN: 0022-0000
DOI: 10.1006/jcss.1997.1388