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author shellac
date Mon, 22 Mar 2021 18:12:50 +0000
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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.

`Wikipedia: Matching <>`_
import networkx as nx

__all__ = ["min_maximal_matching"]

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.

    G : NetworkX graph
      Undirected graph

    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.

    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 $O(|E|)$.

    .. [1] Vazirani, Vijay Approximation Algorithms (2001)
    return nx.maximal_matching(G)