# A Faster Algorithm for the All-Pairs Shortest Path Problem and Its Application

@inproceedings{Takaoka2004AFA, title={A Faster Algorithm for the All-Pairs Shortest Path Problem and Its Application}, author={Tadao Takaoka}, booktitle={COCOON}, year={2004} }

We design a faster algorithm for the all-pairs shortest path problem under the RAM model, based on distance matrix multiplication (DMM). Specifically we improve the best known time complexity of O(n 3(loglog n/log n)1/2) to T(n)=O(n 3(loglog n)2/log n). We extend the algorithm to a parallel algorithm for DMM, whose time complexity is O(log n) and number of processors is T(n)/log n. As an application, we show how to speed up the algorithm for the maximum subarray problem.

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## An O ( n 3 log log n / log n ) Time Algorithm for the All-Pairs Shortest Path Problem

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## A survey of the all-pairs shortest paths problem and its variants in graphs

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## All-Pairs Shortest Paths with Real Weights in O(n3/log n) Time

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## More algorithms for all-pairs shortest paths in weighted graphs

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## A Slightly Improved Sub-Cubic Algorithm for the All Pairs Shortest Paths Problem with Real Edge Lengths

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## Finding a shortest walk along a sequence of imprecise regions in a graph

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