Parameterized Complexity of Graph Constraint Logic
Abstract
Graph constraint logic is a framework introduced by Hearn and Demaine, which provides several problems that are often a convenient starting point for reductions. We study the parameterized complexity of Constraint Graph Satisfiability and both bounded and unbounded versions of Nondeterministic Constraint Logic (NCL) with respect to solution length, treewidth and maximum degree of the underlying constraint graph as parameters. As a main result we show that restricted NCL remains PSPACEcomplete on graphs of bounded bandwidth, strengthening Hearn and Demaine's framework. This allows us to improve upon existing results obtained by reduction from NCL. We show that reconfiguration versions of several classical graph problems (including independent set, feedback vertex set and dominating set) are PSPACEcomplete on planar graphs of bounded bandwidth and that Rush Hour, generalized to $k\times n$ boards, is PSPACEcomplete even when $k$ is at most a constant.
 Publication:

arXiv eprints
 Pub Date:
 September 2015
 arXiv:
 arXiv:1509.02683
 Bibcode:
 2015arXiv150902683V
 Keywords:

 Computer Science  Computational Complexity;
 F.2.2