Fixed-parameter algorithms for graph constraint logic

Tatsuhiko Hatanaka, Felix Hommelsheim, Takehiro Ito, Yusuke Kobayashi, Moritz Mühlenthaler, Akira Suzuki

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Non-deterministic constraint logic (NCL) is a simple model of computation based on orientations of a constraint graph with edge weights and vertex demands. NCL captures PSPACE and has been a useful tool for proving algorithmic hardness of many puzzles, games, and reconfiguration problems. In particular, its usefulness stems from the fact that it remains PSPACE-complete even under severe restrictions of the weights (e.g., only edge-weights one and two are needed) and the structure of the constraint graph (e.g., planar and/or graphs of bounded bandwidth). While such restrictions on the structure of constraint graphs do not seem to limit the expressiveness of NCL, the building blocks of the constraint graphs cannot be limited without losing expressiveness: We consider as parameters the number of weight-one edges and the number of weight-two edges of a constraint graph, as well as the number of and or or vertices of an and/or constraint graph. We show that NCL is fixed-parameter tractable (FPT) for any of these parameters. In particular, for NCL parameterized by the number of weight-one edges or the number of and vertices, we obtain a linear kernel. It follows that, in a sense, NCL as introduced by Hearn and Demaine is defined in the most economical way for the purpose of capturing PSPACE.

Original languageEnglish
Title of host publication15th International Symposium on Parameterized and Exact Computation, IPEC 2020
EditorsYixin Cao, Marcin Pilipczuk
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771726
DOIs
Publication statusPublished - 2020 Dec
Event15th International Symposium on Parameterized and Exact Computation, IPEC 2020 - Virtual, Hong Kong, China
Duration: 2020 Dec 142020 Dec 18

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume180
ISSN (Print)1868-8969

Conference

Conference15th International Symposium on Parameterized and Exact Computation, IPEC 2020
CountryChina
CityVirtual, Hong Kong
Period20/12/1420/12/18

Keywords

  • Combinatorial Reconfiguration
  • Fixed Parameter Tractability
  • Nondeterministic Constraint Logic

ASJC Scopus subject areas

  • Software

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