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Partial vertex cover on graphs of bounded degeneracy
, Article 17th International Computer Science Symposium in Russia, CSR 2022, 29 June 2022 through 1 July 2022 ; Volume 13296 LNCS , 2022 , Pages 289-301 ; 03029743 (ISSN); 9783031095733 (ISBN) ; Yaghoubizade, H ; Sharif University of Technology
Springer Science and Business Media Deutschland GmbH
2022
Abstract
In the Partial Vertex Cover (PVC) problem, we are given an n-vertex graph G and a positive integer k, and the objective is to find a vertex subset S of size k maximizing the number of edges with at least one end-point in S. This problem is W[1]-hard on general graphs, but admits a parameterized subexponential time algorithm with running time 2O(k)nO(1) on planar and apex-minor free graphs [Fomin et al. (FSTTCS 2009, IPL 2011)], and a kO(k)nO(1) time algorithm on bounded degeneracy graphs [Amini et al. (FSTTCS 2009, JCSS 2011)]. Graphs of bounded degeneracy contain many sparse graph classes like planar graphs, H-minor free graphs, and bounded tree-width graphs (see Fig. 1). In this work, we...
Faster Algorithms for Quantitative Analysis of MCs and MDPs with Small Treewidth
, Article 18th International Symposium on Automated Technology for Verification and Analysis, ATVA 2020, 19 October 2020 through 23 October 2020 ; Volume 12302 LNCS , 2020 , Pages 253-270 ; Chatterjee, K ; Kafshdar Goharshady, A ; Mohammadi, K ; Pavlogiannis, A ; Sharif University of Technology
Springer Science and Business Media Deutschland GmbH
2020
Abstract
Discrete-time Markov Chains (MCs) and Markov Decision Processes (MDPs) are two standard formalisms in system analysis. Their main associated quantitative objectives are hitting probabilities, discounted sum, and mean payoff. Although there are many techniques for computing these objectives in general MCs/MDPs, they have not been thoroughly studied in terms of parameterized algorithms, particularly when treewidth is used as the parameter. This is in sharp contrast to qualitative objectives for MCs, MDPs and graph games, for which treewidth-based algorithms yield significant complexity improvements. In this work, we show that treewidth can also be used to obtain faster algorithms for the...