All-Pairs Shortest Paths for Unweighted Undirected Graphs in o(mn) Time

被引：25

作者：

Chan, Timothy M. ^{[1
]}

机构：

[1] Univ Waterloo, Sch Comp Sci, Waterloo, ON N2L 3G1, Canada

来源：

PROCEEDINGS OF THE SEVENTHEENTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS | 2006年

关键词：

D O I：

10.1145/1109557.1109614

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We revisit the all-pairs-shortest-paths problem for an unweighted undirected graph with n vertices and in edges. We present new algorithms with the following running times: {O(mn/log n) if m > n log(2) n O(mn log log n/log n) if m > n log log n O(n(2) log(2) log n/log n) if m <= n log log n. These represent the best time bounds known for the problem for all m << n(1.376). We also obtain a similar type of result for the diameter problem for unweighted directed graphs.

引用

页码：514 / 523

页数：10

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