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Source code for networkx.algorithms.approximation.matching
# -*- coding: utf-8 -*- """ ************** Graph Matching ************** Given a graph G = (V,E), a matching M in G is a set of pairwise non-adjacent edges; that is, no two edges share a common vertex. http://en.wikipedia.org/wiki/Matching_(graph_theory) """ # Copyright (C) 2011-2012 by # Nicholas Mancuso <email@example.com> # All rights reserved. # BSD license. import networkx as nx __all__ = ["min_maximal_matching"] __author__ = """Nicholas Mancuso (firstname.lastname@example.org)"""[docs]def min_maximal_matching(G): r"""Returns the minimum maximal matching of G. That is, out of all maximal matchings of the graph G, the smallest is returned. Parameters ---------- G : NetworkX graph Undirected graph Returns ------- min_maximal_matching : set Returns a set of edges such that no two edges share a common endpoint and every edge not in the set shares some common endpoint in the set. Cardinality will be 2*OPT in the worst case. Notes ----- The algorithm computes an approximate solution fo the minimum maximal cardinality matching problem. The solution is no more than 2 * OPT in size. Runtime is `O(|E|)`. References ---------- ..  Vazirani, Vijay Approximation Algorithms (2001) """ return nx.maximal_matching(G)