56 lines
2.0 KiB
Python
56 lines
2.0 KiB
Python
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""" Functions related to graph covers."""
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from networkx.algorithms.bipartite.matching import hopcroft_karp_matching
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from networkx.algorithms.covering import min_edge_cover as _min_edge_cover
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from networkx.utils import not_implemented_for
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__all__ = ["min_edge_cover"]
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@not_implemented_for("directed")
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@not_implemented_for("multigraph")
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def min_edge_cover(G, matching_algorithm=None):
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"""Returns a set of edges which constitutes
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the minimum edge cover of the graph.
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The smallest edge cover can be found in polynomial time by finding
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a maximum matching and extending it greedily so that all nodes
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are covered.
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Parameters
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----------
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G : NetworkX graph
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An undirected bipartite graph.
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matching_algorithm : function
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A function that returns a maximum cardinality matching in a
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given bipartite graph. The function must take one input, the
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graph ``G``, and return a dictionary mapping each node to its
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mate. If not specified,
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:func:`~networkx.algorithms.bipartite.matching.hopcroft_karp_matching`
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will be used. Other possibilities include
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:func:`~networkx.algorithms.bipartite.matching.eppstein_matching`,
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Returns
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-------
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set
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A set of the edges in a minimum edge cover of the graph, given as
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pairs of nodes. It contains both the edges `(u, v)` and `(v, u)`
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for given nodes `u` and `v` among the edges of minimum edge cover.
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Notes
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-----
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An edge cover of a graph is a set of edges such that every node of
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the graph is incident to at least one edge of the set.
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A minimum edge cover is an edge covering of smallest cardinality.
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Due to its implementation, the worst-case running time of this algorithm
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is bounded by the worst-case running time of the function
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``matching_algorithm``.
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"""
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if G.order() == 0: # Special case for the empty graph
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return set()
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if matching_algorithm is None:
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matching_algorithm = hopcroft_karp_matching
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return _min_edge_cover(G, matching_algorithm=matching_algorithm)
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