Next Article in Journal
Pre and Postprocessing for JPEG to Handle Large Monochrome Images
Next Article in Special Issue
Parameterized Algorithms in Bioinformatics: An Overview
Previous Article in Journal
Walking Gait Phase Detection Based on Acceleration Signals Using LSTM-DNN Algorithm
Previous Article in Special Issue
Solving Integer Linear Programs by Exploiting Variable-Constraint Interactions: A Survey
Open AccessArticle

FPT Algorithms for Diverse Collections of Hitting Sets

Institute of Optimization and Operations Research, Ulm University, 89081 Ulm, Germany
Department of Informatics, University of Bergen, 5008 Bergen, Norway
Department of Applied Mathematics of the Faculty of Mathematics and Physics, Charles University, 11800 Prague, Czech Republic
Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, 02-097 Warszawa, Poland
Chennai Mathematical Institute, Chennai 603103, India
International Joint Unit Research Lab in Computer Science (UMI ReLaX), Chennai 603103, India
Fachbereich Mathematik und Informatik, Freie Universität Berlin, D-14195 Berlin, Germany
Authors to whom correspondence should be addressed.
Algorithms 2019, 12(12), 254;
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 k + r 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. View Full-Text
Keywords: solution diversity; fixed-parameter tractability; hitting sets; vertex cover; feedback vertex set; Hamming distance solution diversity; fixed-parameter tractability; hitting sets; vertex cover; feedback vertex set; Hamming distance
Show Figures

Figure 1

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.

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.

Chicago/Turabian Style

Baste, Julien; Jaffke, Lars; Masařík, Tomáš; Philip, Geevarghese; Rote, Günter. 2019. "FPT Algorithms for Diverse Collections of Hitting Sets" Algorithms 12, no. 12: 254.

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

Search more from Scilit
Back to TopTop