On the Comparison-Addition Complexity of All-Pairs Shortest Paths
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On the Comparison-Addition Complexity of All-Pairs Shortest Paths
We present an all-pairs shortest path algorithm for arbitrary graphs that performs O(mn log ) comparison and addition operations, where m and n are the number of edges and vertices, resp., and = (m;n) is Tarjan's inverse-Ackermann function. Our algorithm eliminates the sorting bottleneck inherent in approaches based on Dijkstra's algorithm, and for graphs with O(n) edges our algorithm is within...
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We investigate the all-pairs shortest paths problem in weighted graphs. We present an algorithm|the Hidden Paths Algorithm|that nds these paths in time O(m n+n 2 log n), where m is the number of edges participating in shortest paths. Our algorithm is a practical substitute for Dijkstra's algorithm. We argue that m is likely to be small in practice, since m = O(n logn) with high probability for ...
متن کاملAll - Pairs Shortest Paths in O ( n 2 ) Time with High Probability
We present an all-pairs shortest path algorithm whose running time on a complete directed graph on n vertices whose edge weights are chosen independently and uniformly at random from [0, 1] is O(n2), in expectation and with high probability. This resolves a long-standing open problem. The algorithm is a variant of the dynamic all-pairs shortest paths algorithm of Demetrescu and Italiano [2006]....
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We introduce a new problem that combines the well known All Pairs Shortest Paths (APSP) problem and the All Pairs Bottleneck Paths (APBP) problem to compute the shortest paths for all pairs of vertices for all possible flow amounts. We call this new problem the All Pairs Shortest Paths for All Flows (APSP-AF) problem. We firstly solve the APSP-AF problem on directed graphs with unit edge costs ...
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Two plausible ways to implement Floyd’s all pairs shortest paths algorithm on a hypercube mutiprocessor are considered. These are evaluated experimentally. A comparison with using Dijkstra’s single source all desitination algorithm on each processor is also done.
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تاریخ انتشار 2002