Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/dominating.py @ 0:4f3585e2f14b draft default tip
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author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |
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1 """Functions for computing dominating sets in a graph.""" |
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2 from itertools import chain |
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3 |
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4 import networkx as nx |
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5 from networkx.utils import arbitrary_element |
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6 |
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7 __all__ = ["dominating_set", "is_dominating_set"] |
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8 |
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9 |
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10 def dominating_set(G, start_with=None): |
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11 r"""Finds a dominating set for the graph G. |
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12 |
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13 A *dominating set* for a graph with node set *V* is a subset *D* of |
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14 *V* such that every node not in *D* is adjacent to at least one |
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15 member of *D* [1]_. |
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16 |
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17 Parameters |
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18 ---------- |
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19 G : NetworkX graph |
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20 |
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21 start_with : node (default=None) |
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22 Node to use as a starting point for the algorithm. |
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23 |
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24 Returns |
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25 ------- |
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26 D : set |
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27 A dominating set for G. |
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28 |
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29 Notes |
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30 ----- |
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31 This function is an implementation of algorithm 7 in [2]_ which |
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32 finds some dominating set, not necessarily the smallest one. |
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33 |
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34 See also |
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35 -------- |
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36 is_dominating_set |
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37 |
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38 References |
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39 ---------- |
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40 .. [1] https://en.wikipedia.org/wiki/Dominating_set |
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41 |
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42 .. [2] Abdol-Hossein Esfahanian. Connectivity Algorithms. |
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43 http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf |
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44 |
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45 """ |
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46 all_nodes = set(G) |
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47 if start_with is None: |
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48 start_with = arbitrary_element(all_nodes) |
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49 if start_with not in G: |
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50 raise nx.NetworkXError(f"node {start_with} is not in G") |
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51 dominating_set = {start_with} |
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52 dominated_nodes = set(G[start_with]) |
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53 remaining_nodes = all_nodes - dominated_nodes - dominating_set |
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54 while remaining_nodes: |
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55 # Choose an arbitrary node and determine its undominated neighbors. |
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56 v = remaining_nodes.pop() |
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57 undominated_neighbors = set(G[v]) - dominating_set |
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58 # Add the node to the dominating set and the neighbors to the |
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59 # dominated set. Finally, remove all of those nodes from the set |
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60 # of remaining nodes. |
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61 dominating_set.add(v) |
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62 dominated_nodes |= undominated_neighbors |
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63 remaining_nodes -= undominated_neighbors |
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64 return dominating_set |
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65 |
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66 |
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67 def is_dominating_set(G, nbunch): |
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68 """Checks if `nbunch` is a dominating set for `G`. |
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69 |
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70 A *dominating set* for a graph with node set *V* is a subset *D* of |
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71 *V* such that every node not in *D* is adjacent to at least one |
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72 member of *D* [1]_. |
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73 |
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74 Parameters |
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76 G : NetworkX graph |
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77 |
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78 nbunch : iterable |
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79 An iterable of nodes in the graph `G`. |
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80 |
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81 See also |
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82 -------- |
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83 dominating_set |
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84 |
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85 References |
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86 ---------- |
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87 .. [1] https://en.wikipedia.org/wiki/Dominating_set |
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88 |
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89 """ |
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90 testset = {n for n in nbunch if n in G} |
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91 nbrs = set(chain.from_iterable(G[n] for n in testset)) |
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92 return len(set(G) - testset - nbrs) == 0 |