## Mercurial > repos > shellac > sam_consensus_v3

### view env/lib/python3.9/site-packages/networkx/algorithms/approximation/dominating_set.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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"""Functions for finding node and edge dominating sets. A `dominating set`_ for an undirected graph *G* with vertex set *V* and edge set *E* is a subset *D* of *V* such that every vertex not in *D* is adjacent to at least one member of *D*. An `edge dominating set`_ is a subset *F* of *E* such that every edge not in *F* is incident to an endpoint of at least one edge in *F*. .. _dominating set: https://en.wikipedia.org/wiki/Dominating_set .. _edge dominating set: https://en.wikipedia.org/wiki/Edge_dominating_set """ from ..matching import maximal_matching from ...utils import not_implemented_for __all__ = ["min_weighted_dominating_set", "min_edge_dominating_set"] # TODO Why doesn't this algorithm work for directed graphs? @not_implemented_for("directed") def min_weighted_dominating_set(G, weight=None): r"""Returns a dominating set that approximates the minimum weight node dominating set. Parameters ---------- G : NetworkX graph Undirected graph. weight : string The node attribute storing the weight of an node. If provided, the node attribute with this key must be a number for each node. If not provided, each node is assumed to have weight one. Returns ------- min_weight_dominating_set : set A set of nodes, the sum of whose weights is no more than `(\log w(V)) w(V^*)`, where `w(V)` denotes the sum of the weights of each node in the graph and `w(V^*)` denotes the sum of the weights of each node in the minimum weight dominating set. Notes ----- This algorithm computes an approximate minimum weighted dominating set for the graph `G`. The returned solution has weight `(\log w(V)) w(V^*)`, where `w(V)` denotes the sum of the weights of each node in the graph and `w(V^*)` denotes the sum of the weights of each node in the minimum weight dominating set for the graph. This implementation of the algorithm runs in $O(m)$ time, where $m$ is the number of edges in the graph. References ---------- .. [1] Vazirani, Vijay V. *Approximation Algorithms*. Springer Science & Business Media, 2001. """ # The unique dominating set for the null graph is the empty set. if len(G) == 0: return set() # This is the dominating set that will eventually be returned. dom_set = set() def _cost(node_and_neighborhood): """Returns the cost-effectiveness of greedily choosing the given node. `node_and_neighborhood` is a two-tuple comprising a node and its closed neighborhood. """ v, neighborhood = node_and_neighborhood return G.nodes[v].get(weight, 1) / len(neighborhood - dom_set) # This is a set of all vertices not already covered by the # dominating set. vertices = set(G) # This is a dictionary mapping each node to the closed neighborhood # of that node. neighborhoods = {v: {v} | set(G[v]) for v in G} # Continue until all vertices are adjacent to some node in the # dominating set. while vertices: # Find the most cost-effective node to add, along with its # closed neighborhood. dom_node, min_set = min(neighborhoods.items(), key=_cost) # Add the node to the dominating set and reduce the remaining # set of nodes to cover. dom_set.add(dom_node) del neighborhoods[dom_node] vertices -= min_set return dom_set def min_edge_dominating_set(G): r"""Returns minimum cardinality edge dominating set. Parameters ---------- G : NetworkX graph Undirected graph Returns ------- min_edge_dominating_set : set Returns a set of dominating edges whose size is no more than 2 * OPT. Notes ----- The algorithm computes an approximate solution to the edge dominating set problem. The result is no more than 2 * OPT in terms of size of the set. Runtime of the algorithm is $O(|E|)$. """ if not G: raise ValueError("Expected non-empty NetworkX graph!") return maximal_matching(G)