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comparison planemo/lib/python3.7/site-packages/networkx/algorithms/covering.py @ 1:56ad4e20f292 draft

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"planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
author guerler
date Fri, 31 Jul 2020 00:32:28 -0400
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0:d30785e31577 1:56ad4e20f292
1 # Copyright 2016-2019 NetworkX developers.
2 # Copyright (C) 2016 by
3 # Nishant Nikhil <nishantiam@gmail.com>
4 # All rights reserved.
5 # BSD license.
6
7 """ Functions related to graph covers."""
8
9 import networkx as nx
10 from networkx.utils import not_implemented_for, arbitrary_element
11 from functools import partial
12 from itertools import chain
13
14
15 __all__ = ['min_edge_cover', 'is_edge_cover']
16
17
18 @not_implemented_for('directed')
19 @not_implemented_for('multigraph')
20 def min_edge_cover(G, matching_algorithm=None):
21 """Returns a set of edges which constitutes
22 the minimum edge cover of the graph.
23
24 A smallest edge cover can be found in polynomial time by finding
25 a maximum matching and extending it greedily so that all nodes
26 are covered.
27
28 Parameters
29 ----------
30 G : NetworkX graph
31 An undirected bipartite graph.
32
33 matching_algorithm : function
34 A function that returns a maximum cardinality matching in a
35 given bipartite graph. The function must take one input, the
36 graph ``G``, and return a dictionary mapping each node to its
37 mate. If not specified,
38 :func:`~networkx.algorithms.bipartite.matching.hopcroft_karp_matching`
39 will be used. Other possibilities include
40 :func:`~networkx.algorithms.bipartite.matching.eppstein_matching`,
41 or matching algorithms in the
42 :mod:`networkx.algorithms.matching` module.
43
44 Returns
45 -------
46 min_cover : set
47
48 It contains all the edges of minimum edge cover
49 in form of tuples. It contains both the edges `(u, v)` and `(v, u)`
50 for given nodes `u` and `v` among the edges of minimum edge cover.
51
52 Notes
53 -----
54 An edge cover of a graph is a set of edges such that every node of
55 the graph is incident to at least one edge of the set.
56 The minimum edge cover is an edge covering of smallest cardinality.
57
58 Due to its implementation, the worst-case running time of this algorithm
59 is bounded by the worst-case running time of the function
60 ``matching_algorithm``.
61
62 Minimum edge cover for bipartite graph can also be found using the
63 function present in :mod:`networkx.algorithms.bipartite.covering`
64 """
65 if nx.number_of_isolates(G) > 0:
66 # ``min_cover`` does not exist as there is an isolated node
67 raise nx.NetworkXException(
68 "Graph has a node with no edge incident on it, "
69 "so no edge cover exists.")
70 if matching_algorithm is None:
71 matching_algorithm = partial(nx.max_weight_matching,
72 maxcardinality=True)
73 maximum_matching = matching_algorithm(G)
74 # ``min_cover`` is superset of ``maximum_matching``
75 try:
76 min_cover = set(maximum_matching.items()) # bipartite matching case returns dict
77 except AttributeError:
78 min_cover = maximum_matching
79 # iterate for uncovered nodes
80 uncovered_nodes = set(G) - {v for u, v in min_cover} - {u for u, v in min_cover}
81 for v in uncovered_nodes:
82 # Since `v` is uncovered, each edge incident to `v` will join it
83 # with a covered node (otherwise, if there were an edge joining
84 # uncovered nodes `u` and `v`, the maximum matching algorithm
85 # would have found it), so we can choose an arbitrary edge
86 # incident to `v`. (This applies only in a simple graph, not a
87 # multigraph.)
88 u = arbitrary_element(G[v])
89 min_cover.add((u, v))
90 min_cover.add((v, u))
91 return min_cover
92
93
94 @not_implemented_for('directed')
95 def is_edge_cover(G, cover):
96 """Decides whether a set of edges is a valid edge cover of the graph.
97
98 Given a set of edges, whether it is an edge covering can
99 be decided if we just check whether all nodes of the graph
100 has an edge from the set, incident on it.
101
102 Parameters
103 ----------
104 G : NetworkX graph
105 An undirected bipartite graph.
106
107 cover : set
108 Set of edges to be checked.
109
110 Returns
111 -------
112 bool
113 Whether the set of edges is a valid edge cover of the graph.
114
115 Notes
116 -----
117 An edge cover of a graph is a set of edges such that every node of
118 the graph is incident to at least one edge of the set.
119 """
120 return set(G) <= set(chain.from_iterable(cover))