FPT Algorithms for Diverse Collections of Hitting Sets
1
Institute of Optimization and Operations Research, Ulm University, 89081 Ulm, Germany
2
Department of Informatics, University of Bergen, 5008 Bergen, Norway
3
Department of Applied Mathematics of the Faculty of Mathematics and Physics, Charles University, 11800 Prague, Czech Republic
4
Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, 02-097 Warszawa, Poland
5
Chennai Mathematical Institute, Chennai 603103, India
6
International Joint Unit Research Lab in Computer Science (UMI ReLaX), Chennai 603103, India
7
Fachbereich Mathematik und Informatik, Freie Universität Berlin, D-14195 Berlin, Germany
*
Authors to whom correspondence should be addressed.
Algorithms 2019, 12(12), 254; https://doi.org/10.3390/a12120254
Received: 25 October 2019 / Revised: 22 November 2019 / Accepted: 23 November 2019 / Published: 27 November 2019
(This article belongs to the Special Issue New Frontiers in Parameterized Complexity and Algorithms)
In this work, we study the d-Hitting Set and Feedback Vertex Set problems through the paradigm of finding diverse collections of r solutions of size at most k each, which has recently been introduced to the field of parameterized complexity. This paradigm is aimed at addressing the loss of important side information which typically occurs during the abstraction process that models real-world problems as computational problems. We use two measures for the diversity of such a collection: the sum of all pairwise Hamming distances, and the minimum pairwise Hamming distance. We show that both problems are fixed-parameter tractable in for both diversity measures. A key ingredient in our algorithms is a (problem independent) network flow formulation that, given a set of ‘base’ solutions, computes a maximally diverse collection of solutions. We believe that this could be of independent interest.
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Keywords:
solution diversity; fixed-parameter tractability; hitting sets; vertex cover; feedback vertex set; Hamming distance
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MDPI and ACS Style
Baste, J.; Jaffke, L.; Masařík, T.; Philip, G.; Rote, G. FPT Algorithms for Diverse Collections of Hitting Sets. Algorithms 2019, 12, 254. https://doi.org/10.3390/a12120254
AMA Style
Baste J, Jaffke L, Masařík T, Philip G, Rote G. FPT Algorithms for Diverse Collections of Hitting Sets. Algorithms. 2019; 12(12):254. https://doi.org/10.3390/a12120254
Chicago/Turabian StyleBaste, Julien; Jaffke, Lars; Masařík, Tomáš; Philip, Geevarghese; Rote, Günter. 2019. "FPT Algorithms for Diverse Collections of Hitting Sets" Algorithms 12, no. 12: 254. https://doi.org/10.3390/a12120254
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