## Mercurial > repos > shellac > sam_consensus_v3

### diff env/lib/python3.9/site-packages/networkx/algorithms/approximation/vertex_cover.py @ 0:4f3585e2f14b draft default tip

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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"

author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |

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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/env/lib/python3.9/site-packages/networkx/algorithms/approximation/vertex_cover.py Mon Mar 22 18:12:50 2021 +0000 @@ -0,0 +1,74 @@ +"""Functions for computing an approximate minimum weight vertex cover. + +A |vertex cover|_ is a subset of nodes such that each edge in the graph +is incident to at least one node in the subset. + +.. _vertex cover: https://en.wikipedia.org/wiki/Vertex_cover +.. |vertex cover| replace:: *vertex cover* + +""" + +__all__ = ["min_weighted_vertex_cover"] + + +def min_weighted_vertex_cover(G, weight=None): + r"""Returns an approximate minimum weighted vertex cover. + + The set of nodes returned by this function is guaranteed to be a + vertex cover, and the total weight of the set is guaranteed to be at + most twice the total weight of the minimum weight vertex cover. In + other words, + + .. math:: + + w(S) \leq 2 * w(S^*), + + where $S$ is the vertex cover returned by this function, + $S^*$ is the vertex cover of minimum weight out of all vertex + covers of the graph, and $w$ is the function that computes the + sum of the weights of each node in that given set. + + Parameters + ---------- + G : NetworkX graph + + weight : string, optional (default = None) + If None, every node has weight 1. If a string, use this node + attribute as the node weight. A node without this attribute is + assumed to have weight 1. + + Returns + ------- + min_weighted_cover : set + Returns a set of nodes whose weight sum is no more than twice + the weight sum of the minimum weight vertex cover. + + Notes + ----- + For a directed graph, a vertex cover has the same definition: a set + of nodes such that each edge in the graph is incident to at least + one node in the set. Whether the node is the head or tail of the + directed edge is ignored. + + This is the local-ratio algorithm for computing an approximate + vertex cover. The algorithm greedily reduces the costs over edges, + iteratively building a cover. The worst-case runtime of this + implementation is $O(m \log n)$, where $n$ is the number + of nodes and $m$ the number of edges in the graph. + + References + ---------- + .. [1] Bar-Yehuda, R., and 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> + + """ + cost = dict(G.nodes(data=weight, default=1)) + # While there are uncovered edges, choose an uncovered and update + # the cost of the remaining edges. + for u, v in G.edges(): + min_cost = min(cost[u], cost[v]) + cost[u] -= min_cost + cost[v] -= min_cost + return {u for u, c in cost.items() if c == 0}