A multivariate approach for weighted FPT algorithms

Hadas Shachnai, Meirav Zehavi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

We introduce a multivariate approach for solving weighted parameterized problems. Building on the flexible use of certain parameters, our approach defines a new general 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 wide applicability of our approach by solving the weighted variants of 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 aWnO(1), for some constant a > 1, our approach yields running times of the form bsnO(1), for some constant b ≤ a, 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. Clearly, s can be substantially smaller than W. Moreover, we give an example for a problem whose polynomialtime solvability crucially relies on our flexible (in lieu of a strict) use of parameters. We further show, among other results, that Weighted VertexCover and Weighted Edge Dominating Set are solvable in times 1.443tnO(1) and 3tnO(1), respectively, where t ≤ s is the minimum size of a solution.

Original languageEnglish
Title of host publicationAlgorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings
EditorsNikhil Bansal, Irene Finocchi
PublisherSpringer Verlag
Pages965-976
Number of pages12
ISBN (Print)9783662483497
DOIs
StatePublished - 1 Jan 2015
Externally publishedYes
Event23rd European Symposium on Algorithms, ESA 2015 - Patras, Greece
Duration: 14 Sep 201516 Sep 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9294
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference23rd European Symposium on Algorithms, ESA 2015
Country/TerritoryGreece
CityPatras
Period14/09/1516/09/15

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