Abstract
We revisit the all-pairs-shortest-paths problem for an unweighted undirected graph with n vertices and m edges. We present new algorithms with the following running times: { O ( mn /log n ) if m > n log n log log log 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.
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