Exploiting dense structures in parameterized complexity

William Lochet, Daniel Lokshtanov, Saket Saurabh, Meirav Zehavi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

Over the past few decades, the study of dense structures from the perspective of approximation algorithms has become a wide area of research. However, from the viewpoint of parameterized algorithm, this area is largely unexplored. In particular, properties of random samples have been successfully deployed to design approximation schemes for a number of fundamental problems on dense structures [Arora et al. FOCS 1995, Goldreich et al. FOCS 1996, Giotis and Guruswami SODA 2006, Karpinksi and Schudy STOC 2009]. In this paper, we fill this gap, and harness the power of random samples as well as structure theory to design kernelization as well as parameterized algorithms on dense structures. In particular, we obtain linear vertex kernels for Edge-Disjoint Paths, Edge Odd Cycle Transversal, Minimum Bisection, d-Way Cut, Multiway Cut and Multicut on everywhere dense graphs. In fact, these kernels are obtained by designing a polynomial-time algorithm when the corresponding parameter is at most Ω(n). Additionally, we obtain a cubic kernel for Vertex-Disjoint Paths on everywhere dense graphs. In addition to kernelization results, we obtain randomized subexponential-time parameterized algorithms for Edge Odd Cycle Transversal, Minimum Bisection, and d-Way Cut. Finally, we show how all of our results (as well as EPASes for these problems) can be de-randomized.

Original languageEnglish
Title of host publication38th International Symposium on Theoretical Aspects of Computer Science, STACS 2021
EditorsMarkus Blaser, Benjamin Monmege
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771801
DOIs
StatePublished - 1 Mar 2021
Event38th International Symposium on Theoretical Aspects of Computer Science, STACS 2021 - Virtual, Saarbrucken, Germany
Duration: 16 Mar 202119 Mar 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume187
ISSN (Print)1868-8969

Conference

Conference38th International Symposium on Theoretical Aspects of Computer Science, STACS 2021
Country/TerritoryGermany
CityVirtual, Saarbrucken
Period16/03/2119/03/21

Keywords

  • Dense graphs
  • Disjoint paths
  • Kernels
  • Odd cycle transversal

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