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Reducing CMSO Model Checking to Highly Connected Graphs

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

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  • Theory of computation → Fixed parameter tractability
Keywords
  • Fixed Parameter Tractability Model Checking Recursive Understanding

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Abstract

Given a Counting Monadic Second Order (CMSO) sentence psi, the CMSO[psi] problem is defined as follows. The input to CMSO[psi] is a graph G, and the objective is to determine whether G |= psi. Our main theorem states that for every CMSO sentence psi, if CMSO[psi] is solvable in polynomial time on "globally highly connected graphs", then CMSO[psi] 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.

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Daniel Lokshtanov, M. S. Ramanujan, Saket Saurabh, and Meirav Zehavi. Reducing CMSO Model Checking to Highly Connected Graphs. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 135:1-135:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.ICALP.2018.135

Author Details

Daniel Lokshtanov
  • University of Bergen, Norway
M. S. Ramanujan
  • University of Warwick, United Kingdom
Saket Saurabh
  • The Institute of Mathematical Sciences, HBNI, Chennai, India
Meirav Zehavi
  • Ben-Gurion University, Israel

Funding

  • Lokshtanov, Daniel: Supported by \emph{Pareto-Optimal Parameterized Algorithms}, ERC Starting Grant 715744
  • Ramanujan, M. S.: Supported by \emph{BeHard}, Bergen Research Foundation and \emph{X-Tract}, Austrian Science Fund (FWF, project P26696)
  • Saurabh, Saket: Supported by \emph{Parameterized Approximation}, ERC Starting Grant 306992.

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