62 lines
2.2 KiB
Python
62 lines
2.2 KiB
Python
# Copyright 2016-2019 NetworkX developers.
|
|
# Copyright (C) 2016 by
|
|
# Nishant Nikhil <nishantiam@gmail.com>
|
|
# All rights reserved.
|
|
# BSD license.
|
|
|
|
""" Functions related to graph covers."""
|
|
|
|
from networkx.utils import not_implemented_for
|
|
from networkx.algorithms.bipartite.matching import hopcroft_karp_matching
|
|
from networkx.algorithms.covering import min_edge_cover as _min_edge_cover
|
|
|
|
__all__ = ['min_edge_cover']
|
|
|
|
|
|
@not_implemented_for('directed')
|
|
@not_implemented_for('multigraph')
|
|
def min_edge_cover(G, matching_algorithm=None):
|
|
"""Returns a set of edges which constitutes
|
|
the minimum edge cover of the graph.
|
|
|
|
The smallest edge cover can be found in polynomial time by finding
|
|
a maximum matching and extending it greedily so that all nodes
|
|
are covered.
|
|
|
|
Parameters
|
|
----------
|
|
G : NetworkX graph
|
|
An undirected bipartite graph.
|
|
|
|
matching_algorithm : function
|
|
A function that returns a maximum cardinality matching in a
|
|
given bipartite graph. The function must take one input, the
|
|
graph ``G``, and return a dictionary mapping each node to its
|
|
mate. If not specified,
|
|
:func:`~networkx.algorithms.bipartite.matching.hopcroft_karp_matching`
|
|
will be used. Other possibilities include
|
|
:func:`~networkx.algorithms.bipartite.matching.eppstein_matching`,
|
|
|
|
Returns
|
|
-------
|
|
set
|
|
A set of the edges in a minimum edge cover of the graph, given as
|
|
pairs of nodes. It contains both the edges `(u, v)` and `(v, u)`
|
|
for given nodes `u` and `v` among the edges of minimum edge cover.
|
|
|
|
Notes
|
|
-----
|
|
An edge cover of a graph is a set of edges such that every node of
|
|
the graph is incident to at least one edge of the set.
|
|
A minimum edge cover is an edge covering of smallest cardinality.
|
|
|
|
Due to its implementation, the worst-case running time of this algorithm
|
|
is bounded by the worst-case running time of the function
|
|
``matching_algorithm``.
|
|
"""
|
|
if G.order() == 0: # Special case for the empty graph
|
|
return set()
|
|
if matching_algorithm is None:
|
|
matching_algorithm = hopcroft_karp_matching
|
|
return _min_edge_cover(G, matching_algorithm=matching_algorithm)
|