TY - JOUR

T1 - Fixed-parameter algorithms for graph constraint logic

AU - Hatanaka, Tatsuhiko

AU - Hommelsheim, Felix

AU - Ito, Takehiro

AU - Kobayashi, Yusuke

AU - Mühlenthaler, Moritz

AU - Suzuki, Akira

N1 - Funding Information:
Tatsuhiko Hatanaka was partially supported by JSPS KAKENHI Grant Number JP16J02175 , Japan. Takehiro Ito was partially supported by JSPS KAKENHI Grant Numbers JP18H04091 , JP19K11814 , and JP20H05793 , Japan. Yusuke Kobayashi was partially supported by JSPS KAKENHI Grant Numbers JP17K19960 , JP18H05291 , JP20H05795 , JP20K11692 , and JP22H05001 , Japan. Akira Suzuki was partially supported by JSPS KAKENHI Grant Numbers JP18H04091 , JP20H05794 , and JP20K11666 , Japan.
Publisher Copyright:
© 2023 Elsevier B.V.

PY - 2023/5/30

Y1 - 2023/5/30

N2 - 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.

AB - 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.

KW - Combinatorial reconfiguration

KW - Fixed-parameter algorithms

KW - Non-deterministic constraint logic

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U2 - 10.1016/j.tcs.2023.113863

DO - 10.1016/j.tcs.2023.113863

M3 - Article

AN - SCOPUS:85153191978

SN - 0304-3975

VL - 959

JO - Theoretical Computer Science

JF - Theoretical Computer Science

M1 - 113863

ER -