A Multivariate Framework for Weighted FPT Algorithms
Journal of Computer and System Sciences(2017)
摘要
We introduce a multivariate approach for solving weighted parameterized problems. By allowing flexible use of parameters, our approach defines a framework for applying the classic bounded search trees technique. In our model, given an instance of size n of a minimization/maximization problem, and a parameter W≥1, we seek a solution of weight at most/at least W. We demonstrate the usefulness of our approach in solving Vertex Cover, 3-Hitting Set, Edge Dominating Set and Max Internal Out-Branching. While the best known algorithms for these problems admit running times of the form cWnO(1), for some c>1, our framework yields running times of the form csnO(1), where s≤W is the minimum size of a solution of weight at most/at least W. If no such solution exists, s=min{W,m}, where m is the maximum size of a solution. In addition, we analyze the parameter t≤s, the minimum size of a solution.
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关键词
Parameterized algorithm,Weighted graph problem,Vertex cover,3-Hitting set,Edge dominating set
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