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Source code for networkx.algorithms.approximation.vertex_cover

# -*- coding: utf-8 -*-
Vertex Cover

Given an undirected graph `G = (V, E)` and a function w assigning nonnegative
weights to its vertices, find a minimum weight subset of V such that each edge
in E is incident to at least one vertex in the subset.

#   Copyright (C) 2011-2012 by
#   Nicholas Mancuso <nick.mancuso@gmail.com>
#   All rights reserved.
#   BSD license.
from networkx.utils import *
__all__ = ["min_weighted_vertex_cover"]
__author__ = """Nicholas Mancuso (nick.mancuso@gmail.com)"""

[docs]def min_weighted_vertex_cover(G, weight=None): r"""2-OPT Local Ratio for Minimum Weighted Vertex Cover Find an approximate minimum weighted vertex cover of a graph. Parameters ---------- G : NetworkX graph Undirected graph weight : None or string, optional (default = None) If None, every edge has weight/distance/cost 1. If a string, use this edge attribute as the edge weight. Any edge attribute not present defaults to 1. Returns ------- min_weighted_cover : set Returns a set of vertices whose weight sum is no more than 2 * OPT. Notes ----- Local-Ratio algorithm for computing an approximate vertex cover. Algorithm greedily reduces the costs over edges and iteratively builds a cover. Worst-case runtime is `O(|E|)`. References ---------- .. [1] Bar-Yehuda, R., & Even, S. (1985). A local-ratio theorem for approximating the weighted vertex cover problem. Annals of Discrete Mathematics, 25, 27–46 http://www.cs.technion.ac.il/~reuven/PDF/vc_lr.pdf """ weight_func = lambda nd: nd.get(weight, 1) cost = dict((n, weight_func(nd)) for n, nd in G.nodes(data=True)) # while there are edges uncovered, continue for u,v in G.edges_iter(): # select some uncovered edge min_cost = min([cost[u], cost[v]]) cost[u] -= min_cost cost[v] -= min_cost return set(u for u in cost if cost[u] == 0)