Average-case complexity of shortest-paths problems in the vertex-potential model

We study the average-case complexity of shortest paths problems in the vertex-potential model. The vertex-potential model is a family of probability distributions on complete directed graphs with arbitrary real edge lengths but without negative cycles. We show that on a graph with n vertices and with respect to this model, the single-source shortest-paths problem can be solved in O(n2) expected time, and the all-pairs shortest-paths problem can be solved in O(n2 log n) expected time.

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