Partially Dynamic Single-Source Shortest Paths on Digraphs with Positive Weights

We examine several structural properties of single-source shortest paths and present a local search algorithm for the partially dynamic single-source shortest paths problem. Our algorithm works on both deterministic digraphs and undirected graphs. For a deterministic digraph with positive arc weights, our algorithm handles a single arc weight increase in \(O(n+\frac{n^2\log n}{m})\) expected time, where n is the number of nodes and m is the number of edges in the digraph. Specifically, our algorithm is an O(n) expected time algorithm when m = Ω(nlogn). This solves partially an open problem proposed by Demetrescu and Italiano (Journal of the ACM. 51(2004), 968–992).

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