Fixed-parameter algorithms for graph constraint logic

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

研究成果: Conference contribution

抄録

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.

本文言語English
ホスト出版物のタイトル15th International Symposium on Parameterized and Exact Computation, IPEC 2020
編集者Yixin Cao, Marcin Pilipczuk
出版社Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN(電子版)9783959771726
DOI
出版ステータスPublished - 2020 12
イベント15th International Symposium on Parameterized and Exact Computation, IPEC 2020 - Virtual, Hong Kong, China
継続期間: 2020 12 142020 12 18

出版物シリーズ

名前Leibniz International Proceedings in Informatics, LIPIcs
180
ISSN(印刷版)1868-8969

Conference

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

ASJC Scopus subject areas

  • ソフトウェア

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