Exact Algorithms for Dominating Clique Problems
نویسندگان
چکیده
We handle in this paper three dominating clique problems, namely, the decision problem itself when one asks if there exists a dominating clique in a graph G and two optimization versions where one asks for a maximumand a minimum-size dominating clique, if any. For the three problems we propose optimal algorithms with provably worst-case upper bounds improving existing ones by (D. Kratsch and M. Liedloff, An exact algorithm for the minimum dominating clique problem, Theoretical Computer Science 385(1-3), pp. 226–240, 2007). We then settle all the three problems in sparse and dense graphs also providing improved upper running time bounds.
منابع مشابه
Fast exact algorithms for some connectivity problems parametrized by clique-width
Given a clique-width expression of a graph G of clique-width k, we provide 2O(k) ·nO(1) time algorithms for connectivity constraints on locally checkable properties such as Connected Dominating Set, Connected Perfect Dominating Set or Node-Weighted Steiner Tree. We also propose an 2O(k) ·nO(1) time algorithm for Feedback Vertex Set. The best running times for all the considered cases were eithe...
متن کاملA Refined Exact Algorithm for Edge Dominating Set
We present an O∗(1.3160n)-time algorithm for the edge dominating set problem in an n-vertex graph, which improves previous exact algorithms for this problem. The algorithm is analyzed by using the “Measure and Conquer method.” We design new branching rules based on conceptually simple local structures, called “clique-producing vertices/cycles,” which significantly simplify the algorithm and its...
متن کاملClique-width: on the price of generality
Many hard problems can be solved efficiently when the input is restricted to graphs of bounded treewidth. By the celebrated result of Courcelle, every decision problem expressible in monadic second order logic is fixed parameter tractable when parameterized by the treewidth of the input graph. Moreover, for every fixed k ≥ 0, such problems can be solved in linear time on graphs of treewidth at ...
متن کاملFaster algorithms for vertex partitioning problems parameterized by clique-width
Many NP-hard problems, such as Dominating Set, are FPT parameterized by clique-width. For graphs of clique-width k given with a kexpression, Dominating Set can be solved in 4knO(1) time. However, no FPT algorithm is known for computing an optimal k-expression. For a graph of clique-width k, if we rely on known algorithms to compute a (23k − 1)expression via rank-width and then solving Dominatin...
متن کاملFaster Algorithms Parameterized by Clique-width
Many NP-hard problems, such as Dominating Set, are FPT parameterized by clique-width. For graphs of clique-width k given with a kexpression, Dominating Set can be solved in 4knO(1) time. However, no FPT algorithm is known for computing an optimal k-expression. For a graph of clique-width k, if we rely on known algorithms to compute a (23k − 1)expression via rank-width and then solving Dominatin...
متن کامل