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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, py_random_state |
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__all__ = ["maximal_independent_set"] |
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@not_implemented_for("directed") |
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@py_random_state(2) |
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@nx._dispatchable |
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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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