43 lines
1.1 KiB
Python
43 lines
1.1 KiB
Python
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"""
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**************
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Graph Matching
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**************
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Given a graph G = (V,E), a matching M in G is a set of pairwise non-adjacent
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edges; that is, no two edges share a common vertex.
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`Wikipedia: Matching <https://en.wikipedia.org/wiki/Matching_(graph_theory)>`_
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"""
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import networkx as nx
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__all__ = ["min_maximal_matching"]
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def min_maximal_matching(G):
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r"""Returns the minimum maximal matching of G. That is, out of all maximal
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matchings of the graph G, the smallest is returned.
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Parameters
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----------
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G : NetworkX graph
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Undirected graph
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Returns
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-------
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min_maximal_matching : set
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Returns a set of edges such that no two edges share a common endpoint
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and every edge not in the set shares some common endpoint in the set.
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Cardinality will be 2*OPT in the worst case.
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Notes
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-----
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The algorithm computes an approximate solution fo the minimum maximal
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cardinality matching problem. The solution is no more than 2 * OPT in size.
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Runtime is $O(|E|)$.
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References
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----------
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.. [1] Vazirani, Vijay Approximation Algorithms (2001)
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"""
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return nx.maximal_matching(G)
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