TY - GEN

T1 - A multivariate approach for weighted FPT algorithms

AU - Shachnai, Hadas

AU - Zehavi, Meirav

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2015.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84945553899&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-48350-3_80

DO - 10.1007/978-3-662-48350-3_80

M3 - Conference contribution

AN - SCOPUS:84945553899

SN - 9783662483497

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 965

EP - 976

BT - Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings

A2 - Bansal, Nikhil

A2 - Finocchi, Irene

PB - Springer Verlag

T2 - 23rd European Symposium on Algorithms, ESA 2015

Y2 - 14 September 2015 through 16 September 2015

ER -