Design and Engineering of External Memory Traversal Algorithms for General Graphs
Algorithmics of Large and Complex Networks
The Floyd--Warshall algorithm on graphs with negative cycles
Information Processing Letters
Sorting under partial information (without the ellipsoid algorithm)
Proceedings of the forty-second ACM symposium on Theory of computing
On table arrangements, scrabble freaks, and jumbled pattern matching
FUN'10 Proceedings of the 5th international conference on Fun with algorithms
More Algorithms for All-Pairs Shortest Paths in Weighted Graphs
SIAM Journal on Computing
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
All-pairs shortest paths for unweighted undirected graphs in o(mn) time
ACM Transactions on Algorithms (TALG)
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
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We describe an O(n3/log n)-time algorithm for the all-pairs-shortest-paths problem for a real-weighted directed graph with n vertices. This slightly improves a series of previous, slightly subcubic algorithms by Fredman (SIAM J. Comput. 5:49–60, 1976), Takaoka (Inform. Process. Lett. 43:195–199, 1992), Dobosiewicz (Int. J. Comput. Math. 32:49–60, 1990), Han (Inform. Process. Lett. 91:245–250, 2004), Takaoka (Proc. 10th Int. Conf. Comput. Comb., Lect. Notes Comput. Sci., vol. 3106, pp. 278–289, Springer, 2004), and Zwick (Proc. 15th Int. Sympos. Algorithms and Computation, Lect. Notes Comput. Sci., vol. 3341, pp. 921–932, Springer, 2004). The new algorithm is surprisingly simple and different from previous ones.