U mde @sHdZddlmZddlZddlmZddgZd ddZej ddZ dS) z3Functions for computing dominating sets in a graph.)chainN)arbitrary_elementdominating_setis_dominating_setcCst|}|dkrt|}||kr2td|d|h}t||}|||}|r|}t|||}||||O}||8}qP|S)a\Finds a dominating set for the graph G. A *dominating set* for a graph with node set *V* is a subset *D* of *V* such that every node not in *D* is adjacent to at least one member of *D* [1]_. Parameters ---------- G : NetworkX graph start_with : node (default=None) Node to use as a starting point for the algorithm. Returns ------- D : set A dominating set for G. Notes ----- This function is an implementation of algorithm 7 in [2]_ which finds some dominating set, not necessarily the smallest one. See also -------- is_dominating_set References ---------- .. [1] https://en.wikipedia.org/wiki/Dominating_set .. [2] Abdol-Hossein Esfahanian. Connectivity Algorithms. http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf Nznode z is not in G)setrnxZ NetworkXErrorpopadd)GZ start_withZ all_nodesrZdominated_nodesZremaining_nodesvZundominated_neighborsr W/home/sam/Atlas/atlas_env/lib/python3.8/site-packages/networkx/algorithms/dominating.pyr s$    csFfdd|D}ttfdd|D}tt||dkS)aChecks if `nbunch` is a dominating set for `G`. A *dominating set* for a graph with node set *V* is a subset *D* of *V* such that every node not in *D* is adjacent to at least one member of *D* [1]_. Parameters ---------- G : NetworkX graph nbunch : iterable An iterable of nodes in the graph `G`. See also -------- dominating_set References ---------- .. [1] https://en.wikipedia.org/wiki/Dominating_set csh|]}|kr|qSr r .0nr r r [sz$is_dominating_set..c3s|]}|VqdS)Nr rrr r \sz$is_dominating_set..r)rr from_iterablelen)r ZnbunchZtestsetZnbrsr rr rCs)N) __doc__ itertoolsrZnetworkxrZnetworkx.utilsr__all__r _dispatchrr r r r s   9