Reducing CMSO model checking to highly connected graphs

Daniel Lokshtanov, M. S. Ramanujan, Saket Saurabh, Meirav Zehavi

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

21 Scopus citations

Abstract

Given a Counting Monadic Second Order (CMSO) sentence ψ, the CMSO[ψ] problem is defined as follows. The input to CMSO[ψ] is a graph G, and the objective is to determine whether G |= ψ. Our main theorem states that for every CMSO sentence ψ, if CMSO[ψ] is solvable in polynomial time on “globally highly connected graphs”, then CMSO[ψ] is solvable in polynomial time (on general graphs). We demonstrate the utility of our theorem in the design of parameterized algorithms. Specifically we show that technical problem-specific ingredients of a powerful method for designing parameterized algorithms, recursive understanding, can be replaced by a black-box invocation of our main theorem. We also show that our theorem can be easily deployed to show fixed parameterized tractability of a wide range of problems, where the input is a graph G and the task is to find a connected induced subgraph of G such that “few” vertices in this subgraph have neighbors outside the subgraph, and additionally the subgraph has a CMSO-definable property.

Original languageEnglish
Title of host publication45th International Colloquium on Automata, Languages, and Programming, ICALP 2018
EditorsChristos Kaklamanis, Daniel Marx, Ioannis Chatzigiannakis, Donald Sannella
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770767
DOIs
StatePublished - 1 Jul 2018
Event45th International Colloquium on Automata, Languages, and Programming, ICALP 2018 - Prague, Czech Republic
Duration: 9 Jul 201813 Jul 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume107
ISSN (Print)1868-8969

Conference

Conference45th International Colloquium on Automata, Languages, and Programming, ICALP 2018
Country/TerritoryCzech Republic
CityPrague
Period9/07/1813/07/18

Keywords

  • Checking recursive understanding
  • Fixed parameter
  • Tractability model

ASJC Scopus subject areas

  • Software

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