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Quantum Algorithms for Matching and Network Flows

Andris Ambainis·Robert Spalek
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Abstract

We present quantum algorithms for the following graph problems: finding a maximal bipartite matching in time O(n sqrt{m+n} log n), finding a maximal non-bipartite matching in time O(n^2 (sqrt{m/n} + log n) log n), and finding a maximal flow in an integer network in time O(min(n^{7/6} sqrt m * U^{1/3}, sqrt{n U} m) log n), where n is the number of vertices, m is the number of edges, and U <= n^{1/4} is an upper bound on the capacity of an edge.

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Andris Ambainis, Robert Spalek. 2005-09-08. Quantum Algorithms for Matching and Network Flows. https://arxiv.org/abs/quant-ph/0508205

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