A new polynomial-time algorithm for linear programming
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On the complexity of local search
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On finding and verifying locally optimal solutions
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Simple local search problems that are hard to solve
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The complexity of the Lin-Kernighan heuristic for the traveling salesman problem
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On the complexity of the parity argument and other inefficient proofs of existence
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Integer Linear Programs and Local Search for Max-Cut
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New Results on the Old k-opt Algorithm for the Traveling Salesman Problem
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Local Search in Combinatorial Optimization
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Annals of Mathematics and Artificial Intelligence
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FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
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)
Inapproximability of pure nash equilibria
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Structure in locally optimal solutions
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
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Journal of the ACM (JACM)
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Journal of the ACM (JACM)
k-means requires exponentially many iterations even in the plane
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SIAM Journal on Computing
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ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
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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
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Congestion games with player-specific constants
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On the PLS-complexity of maximum constraint assignment
Theoretical Computer Science
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In this paper, we survey the research on the complexity of computing locally optimal solutions. We revisit well-known and successful local search heuristics and present results on the complexity of the frequently used standard local search algorithm for various problems. Here, our focus in on worst case, average case, and smoothed complexity along with the existence of sequences of improving steps of exponential length. For a more theoretical investigation, we revisit the framework of PLS and mostly concentrate on the research on CongestionGames, which sparked the interconnection between local search and game theory. We conclude by stating various open problems.