95 lines
2.6 KiB
Python
95 lines
2.6 KiB
Python
"""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"]
|
|
|
|
|
|
@nx._dispatchable
|
|
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_nbrs = 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_nbrs
|
|
remaining_nodes -= undominated_nbrs
|
|
return dominating_set
|
|
|
|
|
|
@nx._dispatchable
|
|
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
|