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annotate planemo/lib/python3.7/site-packages/networkx/algorithms/dominating.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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1 # -*- coding: utf-8 -*-
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2 """Functions for computing dominating sets in a graph."""
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3 from itertools import chain
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4
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5 import networkx as nx
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6 from networkx.utils import arbitrary_element
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7
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8 __author__ = '\n'.join(['Jordi Torrents <jtorrents@milnou.net>'])
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9 __all__ = ['dominating_set', 'is_dominating_set']
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10
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11
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12 def dominating_set(G, start_with=None):
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13 r"""Finds a dominating set for the graph G.
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14
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15 A *dominating set* for a graph with node set *V* is a subset *D* of
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16 *V* such that every node not in *D* is adjacent to at least one
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17 member of *D* [1]_.
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18
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19 Parameters
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20 ----------
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21 G : NetworkX graph
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22
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23 start_with : node (default=None)
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24 Node to use as a starting point for the algorithm.
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25
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26 Returns
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27 -------
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28 D : set
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29 A dominating set for G.
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30
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31 Notes
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32 -----
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33 This function is an implementation of algorithm 7 in [2]_ which
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34 finds some dominating set, not necessarily the smallest one.
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35
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36 See also
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37 --------
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38 is_dominating_set
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39
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40 References
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41 ----------
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42 .. [1] https://en.wikipedia.org/wiki/Dominating_set
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43
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44 .. [2] Abdol-Hossein Esfahanian. Connectivity Algorithms.
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45 http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
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46
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47 """
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48 all_nodes = set(G)
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49 if start_with is None:
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50 start_with = arbitrary_element(all_nodes)
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51 if start_with not in G:
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52 raise nx.NetworkXError('node {} is not in G'.format(start_with))
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53 dominating_set = {start_with}
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54 dominated_nodes = set(G[start_with])
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55 remaining_nodes = all_nodes - dominated_nodes - dominating_set
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56 while remaining_nodes:
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57 # Choose an arbitrary node and determine its undominated neighbors.
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58 v = remaining_nodes.pop()
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59 undominated_neighbors = set(G[v]) - dominating_set
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60 # Add the node to the dominating set and the neighbors to the
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61 # dominated set. Finally, remove all of those nodes from the set
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62 # of remaining nodes.
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63 dominating_set.add(v)
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64 dominated_nodes |= undominated_neighbors
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65 remaining_nodes -= undominated_neighbors
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66 return dominating_set
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67
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68
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69 def is_dominating_set(G, nbunch):
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70 """Checks if `nbunch` is a dominating set for `G`.
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71
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72 A *dominating set* for a graph with node set *V* is a subset *D* of
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73 *V* such that every node not in *D* is adjacent to at least one
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74 member of *D* [1]_.
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75
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76 Parameters
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77 ----------
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78 G : NetworkX graph
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79
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80 nbunch : iterable
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81 An iterable of nodes in the graph `G`.
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82
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83 See also
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84 --------
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85 dominating_set
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86
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87 References
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88 ----------
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89 .. [1] https://en.wikipedia.org/wiki/Dominating_set
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90
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91 """
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92 testset = set(n for n in nbunch if n in G)
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93 nbrs = set(chain.from_iterable(G[n] for n in testset))
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94 return len(set(G) - testset - nbrs) == 0