Abstract
In the present paper we improve Spira's algorithm for the all shortest distance problem and reduce the expected computing time from 0(n 2 log 2 n) to 0(n 2 lognloglogn) where n is the number of vertices in a graph. We also give an algorithm for distance matrix multiplication with 0(n 2 logn) comparisons and additions between distances where n is the dimension of matrices.
On leave from Ibaraki University, Hitachi, Japan
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References
E.W. Dijkstra, “A note on two problems in connection with graphs,” Numer. Math. 1, pp 269–271, (1959).
P.M. Spira, “A new algorithm for finding all shortest paths in a graph of positive arcs in average time 0(n 2 log 2 n),” SIAM Journal, Computing 2, pp 28–32, (1973).
J.S. Carson and A.M. Law, “A note on Spira's algorithm for the all pairs shortest path problem,” SIAM Journal, Computing 6, pp 696–699, (1977).
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© 1980 Springer-Verlag Berlin Heidelberg
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Takaoka, T., Moffat, A. (1980). An 0(n 2 lognloglogn) expected time algorithm for the all shortest distance problem. In: Dembiński, P. (eds) Mathematical Foundations of Computer Science 1980. MFCS 1980. Lecture Notes in Computer Science, vol 88. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022539
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DOI: https://doi.org/10.1007/BFb0022539
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