On the complexity of the parity argument and other inefficient proofs of existence
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
On the Road to $\mathcal{PLS}$-Completeness: 8 Agents in a Singleton Congestion Game
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Integer Programming: Optimization and Evaluation Are Equivalent
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
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
Local search: simple, successful, but sometimes sluggish
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Settling the complexity of local max-cut (almost) completely
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
A survey of approximation results for local search algorithms
Efficient Approximation and Online Algorithms
On the power of nodes of degree four in the local max-cut problem
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
On the PLS-complexity of maximum constraint assignment
Theoretical Computer Science
Discrete Applied Mathematics
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A class of local search problems, PLS (polynomial-time local search), as defined by D.S. Johnson et al. (see J. Comput. Syst. Sci., vol.37, no.1, p.79-100 (1988)) is considered. PLS captures much of the structure of NP problems at the level of their feasible solutions and neighborhoods. It is first shown that CNF (conjunctive normal form) satisfiability is PLS-complete, even with simultaneously bounded size clauses and bounded number of occurrences of variables. This result is used to show that traveling salesman under the k-opt neighborhood is also PLS-complete. It is argued that PLS-completeness is the normal behavior of NP-complete problems.