Fixed-parameter algorithms for graph constraint logic

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 particu...

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Bibliographic Details
Published in:Theoretical computer science Vol. 959; p. 113863
Main Authors: Hatanaka, Tatsuhiko, Hommelsheim, Felix, Ito, Takehiro, Kobayashi, Yusuke, Mühlenthaler, Moritz, Suzuki, Akira
Format: Journal Article
Language:English
Published: Elsevier B.V 30.05.2023
Subjects:
Combinatorial reconfiguration
Fixed-parameter algorithms
Non-deterministic constraint logic
Combinatorial reconfiguration
Non-deterministic constraint logic
Fixed-parameter algorithms
ISSN:0304-3975
Online Access:Get full text
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Summary: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.
ISSN:0304-3975
DOI:10.1016/j.tcs.2023.113863