A multivariate framework for weighted FPT algorithms

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...

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Veröffentlicht in:Journal of computer and system sciences Jg. 89; S. 157 - 189
Hauptverfasser: Shachnai, Hadas, Zehavi, Meirav
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.11.2017
Schlagworte:
3-Hitting set
Edge dominating set
Parameterized algorithm
Vertex cover
Weighted graph problem
Vertex cover
Weighted graph problem
Parameterized algorithm
3-Hitting set
Edge dominating set
ISSN:0022-0000, 1090-2724
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Zusammenfassung: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. •A new multivariate approach for solving weighted parameterized problems.•A general framework for applying the classic bounded search trees technique.•Improved algorithms for weighted versions of VC, 3-HS, EDS and Max IST.
ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2017.05.003