Quantum Algorithms for Matching and Network Flows
Quantum Physics
2007-05-23 v2
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.
Cite
@article{arxiv.quant-ph/0508205,
title = {Quantum Algorithms for Matching and Network Flows},
author = {Andris Ambainis and Robert Spalek},
journal= {arXiv preprint arXiv:quant-ph/0508205},
year = {2007}
}
Comments
13 pages, v2: added an Omega(n^2) lower bound for network flows