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Shortest-path problem is not harder than matrix multiplication. (English) Zbl 0454.68069


MSC:

68R10 Graph theory (including graph drawing) in computer science
68Q25 Analysis of algorithms and problem complexity
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C38 Paths and cycles
05C20 Directed graphs (digraphs), tournaments
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References:

[1] Aho, A.; Hopcroft, J.; Ullman, J., The Design and Analysis of Computer Algorithms (1974), Addison-Wesley: Addison-Wesley Reading, MA
[2] Fisher, M. J.; Meyer, A. R., Boolean matrix multiplication and transitive closure, Proc. \(12^{th}\) Annual Symposium on Switching and Automata Theory, 129-131 (1971)
[3] Pan, V. Ya., Field extension and trilinear aggregating, uniting and canceling for the acceleration of matrix multiplication, Proc. \(20^{th}\) Annual Symposium on Foundation of Computer Science, 28-38 (1979)
[5] Schönhage, A., Partial and total matrix multiplication, (Internal Report (1980), University of Tübingen) · Zbl 0462.68018
[6] Strassen, V., Gaussian elimination is not optimal, Numer. Math., 13, 354-356 (1969) · Zbl 0185.40101
[7] Yuval, G., An algorithm for finding all the shortest paths using \(N^{2.81}\) infinite-precision multiplications, Information Processing Lett., 4, 155-156 (1976) · Zbl 0333.68034
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