Finding the Hidden Path: Time Bounds for All-Pairs Shortest Paths

@inproceedings{Karger1991FindingTH,
  title={Finding the Hidden Path: Time Bounds for All-Pairs Shortest Paths},
  author={David R. Karger and Daphne Koller and Steven J. Phillips},
  booktitle={FOCS},
  year={1991}
}
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 many probability distributions on edge weights. We also prove an (mn) lower bound on the running time… CONTINUE READING
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