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