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# 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} }

- Published 1991 in FOCS
DOI:10.1109/SFCS.1991.185419

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 timeâ€¦Â CONTINUE READING

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