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Partial vertex cover on graphs of bounded degeneracy

Panolan, F ; Sharif University of Technology | 2022

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  1. Type of Document: Article
  2. DOI: 10.1007/978-3-031-09574-0_18
  3. Publisher: Springer Science and Business Media Deutschland GmbH , 2022
  4. Abstract:
  5. 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 prove the following results: There are algorithms for PVC on graphs of degeneracy d with running time 2 O(dk)nO(1) and (e+ ed) k2 o(k)nO(1) which are improvements on the previous kO(k)nO(1) time algorithm by Amini et al. [2]PVC admits a polynomial compression on graphs of bounded degeneracy, resolving an open problem posed by Amini et al. [2]. © 2022, Springer Nature Switzerland AG
  6. Keywords:
  7. Bounded Degeneracy ; Parameterized Algorithms ; Planar Graphs ; Parameter estimation ; Parameterization ; Trees (mathematics) ; Free graphs ; N-vertex graph ; Parameterized algorithm ; Partial vertex cover ; Planar graph ; Running time ; Time algorithms ; Vertex cover ; Vertex Cover problems ; Graphic methods
  8. Source: 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)
  9. URL: https://link.springer.com/chapter/10.1007/978-3-031-09574-0_18