Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
On the complexity of local search
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STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
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The Complexity of Boolean Constraint Satisfaction Local Search Problems
Annals of Mathematics and Artificial Intelligence
Theoretical Aspects of Local Search (Monographs in Theoretical Computer Science. An EATCS Series)
Theoretical Aspects of Local Search (Monographs in Theoretical Computer Science. An EATCS Series)
Structure in locally optimal solutions
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Local search: simple, successful, but sometimes sluggish
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
A survey of approximation results for local search algorithms
Efficient Approximation and Online Algorithms
On the complexity of local search for weighted standard set problems
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
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In this paper, we investigate the complexity of computing locally optimal solutions for the local search problem Maximum Constraint Assignment (MCA). For our investigation, we use the framework of PLS, as defined by Johnson et al. (1988) [9]. In a nutshell, the MCA-problem is a local search version of weighted, generalized MaxSat on constraints (functions mapping assignments to integers) over variables with higher valence; additional parameters in (p,q,r)- MCA simultaneously limit the maximum length p of each constraint, the maximum appearance q of each variable and its valence r. We focus on hardness results and show PLS-completeness of (3,2,3)-MCA and (2,3,6)-MCA using tight reductions from Circuit/Flip. Our results are optimal in the sense that (2,2,r)- MCA is solvable in polynomial time for every r@?N. We also pay special attention to the case of binary variables and show that (6,2,2)- MCA is tight PLS-complete. For our results, we extend and refine a technique from Krentel (1989) [10].