93 lines
2.6 KiB
Python
93 lines
2.6 KiB
Python
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"""Functions for computing dominating sets in a graph."""
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from itertools import chain
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import networkx as nx
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from networkx.utils import arbitrary_element
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__all__ = ["dominating_set", "is_dominating_set"]
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def dominating_set(G, start_with=None):
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r"""Finds a dominating set for the graph G.
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A *dominating set* for a graph with node set *V* is a subset *D* of
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*V* such that every node not in *D* is adjacent to at least one
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member of *D* [1]_.
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Parameters
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----------
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G : NetworkX graph
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start_with : node (default=None)
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Node to use as a starting point for the algorithm.
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Returns
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-------
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D : set
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A dominating set for G.
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Notes
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-----
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This function is an implementation of algorithm 7 in [2]_ which
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finds some dominating set, not necessarily the smallest one.
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See also
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--------
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is_dominating_set
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References
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----------
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.. [1] https://en.wikipedia.org/wiki/Dominating_set
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.. [2] Abdol-Hossein Esfahanian. Connectivity Algorithms.
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http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
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"""
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all_nodes = set(G)
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if start_with is None:
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start_with = arbitrary_element(all_nodes)
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if start_with not in G:
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raise nx.NetworkXError(f"node {start_with} is not in G")
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dominating_set = {start_with}
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dominated_nodes = set(G[start_with])
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remaining_nodes = all_nodes - dominated_nodes - dominating_set
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while remaining_nodes:
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# Choose an arbitrary node and determine its undominated neighbors.
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v = remaining_nodes.pop()
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undominated_neighbors = set(G[v]) - dominating_set
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# Add the node to the dominating set and the neighbors to the
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# dominated set. Finally, remove all of those nodes from the set
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# of remaining nodes.
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dominating_set.add(v)
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dominated_nodes |= undominated_neighbors
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remaining_nodes -= undominated_neighbors
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return dominating_set
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def is_dominating_set(G, nbunch):
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"""Checks if `nbunch` is a dominating set for `G`.
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A *dominating set* for a graph with node set *V* is a subset *D* of
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*V* such that every node not in *D* is adjacent to at least one
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member of *D* [1]_.
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Parameters
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----------
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G : NetworkX graph
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nbunch : iterable
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An iterable of nodes in the graph `G`.
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See also
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--------
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dominating_set
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References
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----------
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.. [1] https://en.wikipedia.org/wiki/Dominating_set
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"""
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testset = {n for n in nbunch if n in G}
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nbrs = set(chain.from_iterable(G[n] for n in testset))
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return len(set(G) - testset - nbrs) == 0
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