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Recently we submitted a paper, whose title is A New Fast Unweighted All-pairsShortest Path Search Algorithm Based on Pruning by Shortest Path Trees, toarXiv. This is related to unweighted graphs. This paper also presents a newfast all-pairs shortest path algorithm for weighted graph based on the sameidea. In Dijkstra algorithm which is said to be fast in weighted graphs, theaverage number of accesses to adjacent vertices (expressed by {\alpha}) isabout equal to the average degree of the graph. On the other hand, ouralgorithm utilizes the shortest path trees of adjacent vertices of each sourcevertex in the same manner as the algorithm for unweighted graphs, and reduce{\alpha} drastically in comparison with Dijkstra algorithm. Roughly speaking{\alpha} is reduced to the value close to 1, because the average degree of atree is about 2, and one is used to come in and the other is used to go out,although that does not hold true when the depth of the short path trees issmall. In case of weighted graphs, a problem which does not occur in unweightedgraphs occurs. It is waiting for the generation of the shortest path tree of anadjacent vertex. Therefore, it is possible that a deadlock occurs. We prove ouralgorithm is deadlock-free. We compared our algorithm with Dijkstra and Pengalgorithms. On Dijkstra algorithm ours outperforms it on speed and {\alpha}except that Dijkstra algorithm slightly outperforms ours or they are almost thesame on CPU time in sparse scale-free graphs. The result on Peng algorithm isas follows: In speed and {\alpha}, ours outperforms Peng algorithm inhypercube-shaped and dense scale-free graphs, but conversely Peng algorithmoutperforms ours in sparse scale-free graphs.

A New Fast Weighted All-pairs Shortest Path Search Algorithm Based on Pruning by Shortest Path Trees