78 lines
2.3 KiB
Python
78 lines
2.3 KiB
Python
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"""
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Algorithm to find a maximal (not maximum) independent set.
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"""
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import networkx as nx
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from networkx.utils import not_implemented_for
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from networkx.utils import py_random_state
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__all__ = ["maximal_independent_set"]
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@py_random_state(2)
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@not_implemented_for("directed")
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def maximal_independent_set(G, nodes=None, seed=None):
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"""Returns a random maximal independent set guaranteed to contain
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a given set of nodes.
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An independent set is a set of nodes such that the subgraph
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of G induced by these nodes contains no edges. A maximal
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independent set is an independent set such that it is not possible
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to add a new node and still get an independent set.
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Parameters
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----------
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G : NetworkX graph
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nodes : list or iterable
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Nodes that must be part of the independent set. This set of nodes
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must be independent.
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seed : integer, random_state, or None (default)
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Indicator of random number generation state.
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See :ref:`Randomness<randomness>`.
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Returns
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-------
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indep_nodes : list
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List of nodes that are part of a maximal independent set.
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Raises
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------
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NetworkXUnfeasible
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If the nodes in the provided list are not part of the graph or
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do not form an independent set, an exception is raised.
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NetworkXNotImplemented
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If `G` is directed.
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Examples
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--------
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>>> G = nx.path_graph(5)
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>>> nx.maximal_independent_set(G) # doctest: +SKIP
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[4, 0, 2]
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>>> nx.maximal_independent_set(G, [1]) # doctest: +SKIP
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[1, 3]
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Notes
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-----
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This algorithm does not solve the maximum independent set problem.
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"""
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if not nodes:
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nodes = {seed.choice(list(G))}
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else:
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nodes = set(nodes)
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if not nodes.issubset(G):
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raise nx.NetworkXUnfeasible(f"{nodes} is not a subset of the nodes of G")
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neighbors = set.union(*[set(G.adj[v]) for v in nodes])
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if set.intersection(neighbors, nodes):
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raise nx.NetworkXUnfeasible(f"{nodes} is not an independent set of G")
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indep_nodes = list(nodes)
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available_nodes = set(G.nodes()).difference(neighbors.union(nodes))
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while available_nodes:
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node = seed.choice(list(available_nodes))
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indep_nodes.append(node)
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available_nodes.difference_update(list(G.adj[node]) + [node])
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return indep_nodes
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