The upper bound on the exponent, |, 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 t
A new upper bound on the complexity of the all pairs shortest path problem
โ Scribed by Tadao Takaoka
- Book ID
- 107766067
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 262 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0020-0190
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๐ SIMILAR VOLUMES
We present an algorithm, APD, that solves the distance version of the all-pairs-shortest-path problem for undirected, unweighted \(n\)-vertex graphs in time \(O(M(n) \log n)\), where \(M(n)\) denotes the time necessary to multiply two \(n \times n\) matrices of small integers (which is currently kno
We review how to solve the all-pairs shortest-path problem in a nonnegatively ลฝ 2 . weighted digraph with n vertices in expected time O n log n . This bound is shown to hold with high probability for a wide class of probability distributions on nonnegatively weighted ลฝ . digraphs. We also prove that