Abstract
We present an all-pairs shortest path algorithm whose running time on a complete directed graph on n vertices whose edge weights are chosen independently and uniformly at random from [0, 1] is O(n2), in expectation and with high probability. This resolves a long-standing open problem. The algorithm is a variant of the dynamic all-pairs shortest paths algorithm of Demetrescu and Italiano [2006]. The analysis relies on a proof that the number of locally shortest paths in such randomly weighted graphs is O(n2), in expectation and with high probability. We also present a dynamic version of the algorithm that recomputes all shortest paths after a random edge update in O(log2 n) expected time.
Original language | English |
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Article number | 26 |
Journal | Journal of the ACM |
Volume | 60 |
Issue number | 4 |
DOIs | |
State | Published - Aug 2013 |
Keywords
- Probabilistic analysis
- Shortest paths