The parameterized complexity of local consistency

  • Authors:

  • Serge Gaspers;Stefan Szeider

  • Affiliations:

  • Institute of Information Systems, Vienna University of Technology, Vienna, Austria;Institute of Information Systems, Vienna University of Technology, Vienna, Austria

  • Venue:
  • CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
  • Year:
  • 2011

Quantified Score

Hi-index 0.00

Visualization

Abstract

We investigate the parameterized complexity of deciding whether a constraint network is k-consistent. We show that, parameterized by k, the problem is complete for the complexity class co-W[2]. As secondary parameters we consider the maximum domain size d and the maximum number l of constraints in which a variable occurs. We show that parameterized by k + d, the problem drops down one complexity level and becomes co-W[1]-complete. Parameterized by k +d+l the problem drops down one more level and becomes fixed-parameter tractable. We further show that the same complexity classification applies to strong k-consistency, directional k-consistency, and strong directional k-consistency. Our results establish a super-polynomial separation between input size and time complexity. Thus we strengthen the known lower bounds on time complexity of k-consistency that are based on input size.