The Complexity of the Lin–Kernighan Heuristic for the Traveling Salesman Problem

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Previous article Next article The Complexity of the Lin–Kernighan Heuristic for the Traveling Salesman ProblemChristos H. PapadimitriouChristos H. Papadimitriouhttps://doi.org/10.1137/0221030PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractIt is shown that finding a local optimum solution with respect to the Lin–Kernighan heuristic for the traveling salesman problem is PLS-complete, and thus as hard as any local search problem.[1] J. L. Bentley, Invited Talk at the First SIAM Symposium on Discrete Algorithms, 1990 Google Scholar[2] Michael R. Garey and , David S. Johnson, Computers and intractability, W. H. Freeman and Co., San Francisco, Calif., 1979x+338, A Guide to the Theory of NP-completeness 80g:68056 0411.68039 Google Scholar[3] J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Nat. Acad. Sci. U.S.A., 79 (1982), 2554–2558 83g:92024 CrossrefISIGoogle Scholar[4] D. S. Johnson, , C. H. Papadimitriou and , M. Yannakakis, How easy is local search?, Proceedings of Foundations of Computer Science, 1985, also in J. CSS. 37 (1988), pp. 79–100 Google Scholar[5] B. W. Kernighan and , S. Lin, An efficient heuristic procedure for partitioning graphs, Bell S. T. J., 49 (1970), 291–307 0333.05001 CrossrefGoogle Scholar[6] M. W. Krentel, On Finding Locally Optimal Solutions, Proceedings of the 4th Structures Conference, 1989 Google Scholar[7] M. W. Krentel, 1989, manuscript Google Scholar[8] S. Lin and , B. W. Kernighan, An effective heuristic algorithm for the traveling-salesman problem, Operations Res., 21 (1973), 498–516 50:12194 0256.90038 CrossrefISIGoogle Scholar[9] G. Lueker, 1975, manuscript, Princeton University, Princeton, NJ Google Scholar[10] N. Megiddo and , C. H. Papadimitriou, On total functions, existence theorems and computational complexity, Theoret. Comput. Sci., 81 (1981), 317–324 10.1016/0304-3975(91)90200-L CrossrefISIGoogle Scholar[11] C. H. Papadimitriou, On graph-theoretic lemmata and complexity classes, Proceedings on Foundations of Computer Science, 1990 Google Scholar[12] Christos H. Papadimitriou and , Kenneth Steiglitz, Combinatorial optimization: algorithms and complexity, Prentice-Hall Inc., Englewood Cliffs, N.J., 1982xvi+496 84k:90036 0503.90060 Google Scholar[13] C. H. Papadimitriou, , A. A. Schäffer and , M. Yannakakis, On the complexity of local search, Proc. STOC Conference, 1990 Google Scholar[14] Alejandro A. Schäffer and , Mihalis Yannakakis, Simple local search problems that are hard to solve, SIAM J. Comput., 20 (1991), 56–87 10.1137/0220004 91k:68065 0716.68048 LinkISIGoogle ScholarKeywordslocal searchtraveling salesman problemPLS-complete Previous article Next article FiguresRelatedReferencesCited ByDetails A discrete cuckoo search algorithm for traveling salesman problem and its application in cutting path optimizationComputers & Industrial Engineering, Vol. 169 | 1 Jul 2022 Cross Ref The complexity of gradient descent: CLS = PPAD ∩ PLSProceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing | 15 June 2021 Cross Ref Exploring Large and Complex Environments Fast and Efficiently2021 IEEE International Conference on Robotics and Automation (ICRA) | 30 May 2021 Cross Ref Studying Heuristics Adaptation to a Specific Degree of Fuzziness2020 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) | 1 Jul 2020 Cross Ref Hierarchical Coverage Path Planning in Complex 3D Environments2020 IEEE International Conference on Robotics and Automation (ICRA) | 1 May 2020 Cross Ref Computational Aspects of the Colorful Carathéodory TheoremDiscrete & Computational Geometry, Vol. 60, No. 3 | 14 March 2018 Cross Ref PPP-Completeness with Connections to Cryptography2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS) | 1 Oct 2018 Cross Ref Das Traveling-Salesman-ProblemKombinatorische Optimierung | 25 July 2018 Cross Ref The Traveling Salesman ProblemCombinatorial Opt