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Greed Is Slow on Sparse Graphs of Oriented Valued Constraints

Authors Artem Kaznatcheev , Sofia Vazquez Alferez

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ACM Subject Classification
  • Theory of computation → Constraint and logic programming
Keywords
  • valued constraint satisfaction problem
  • local search
  • algorithm analysis
  • constraint graphs

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Abstract

Greedy local search is especially popular for solving valued constraint satisfaction problems (VCSPs). Since any method will be slow for some VCSPs, we ask: what is the simplest VCSP on which greedy local search is slow? We construct a VCSP on 6n Boolean variables for which greedy local search takes 7(2ⁿ - 1) steps to find the unique peak. Our VCSP is simple in two ways. First, it is very sparse: its constraint graph has pathwidth 2 and maximum degree 3. This is the simplest VCSP on which some local search could be slow. Second, it is "oriented" – there is an ordering on the variables such that later variables are conditionally-independent of earlier ones. Being oriented allows many non-greedy local search methods to find the unique peak in a quadratic number of steps. Thus, we conclude that - among local search methods - greed is particularly slow.

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Artem Kaznatcheev and Sofia Vazquez Alferez. Greed Is Slow on Sparse Graphs of Oriented Valued Constraints. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 18:1-18:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CP.2025.18

Author Details

Artem Kaznatcheev
  • Department of Mathematics, and Department of Information and Computing Sciences, Utrecht University, The Netherlands
Sofia Vazquez Alferez
  • Department of Mathematics, and Department of Information and Computing Sciences, Utrecht University, The Netherlands

Acknowledgements

We want to thank Martin C. Cooper for his comments which greatly improved the quality of our writing and Melle van Marle for his insightful discussions.

References

  1. Emile Aarts and Jan Karel Lenstra, editors. Local Search in Combinatorial Optimization. Princeton University Press, Princeton, NJ, USA, 2003. Google Scholar
  2. Umberto Bertelè and Francesco Brioschi. On non-serial dynamic programming. Journal of Combinatorial Theory, Series A, 14(2):137-148, 1973. URL: https://doi.org/10.1016/0097-3165(73)90016-2.
  3. Michaela Borzechowski. The complexity class polynomial local search (pls) and pls-complete problems. Bachelor’s thesis, Freie Universitat Berlin, 2016. URL: https://www.mi.fu-berlin.de/inf/groups/ag-ti/theses/download/Borzechowski16.pdf.
  4. Clément Carbonnel, Miguel Romero, and Stanislav Živný. The complexity of general-valued constraint satisfaction problems seen from the other side. SIAM Journal on Computing, 51(1):19-69, 2022. URL: https://doi.org/10.1137/19M1250121.
  5. David A Cohen, Martin C Cooper, Artem Kaznatcheev, and Mark Wallace. Steepest ascent can be exponential in bounded treewidth problems. Operations Research Letters, 48:217-224, 2020. URL: https://doi.org/10.1016/j.orl.2020.02.010.
  6. Marek Cygan, Fedor V Fomin, Łukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michał Pilipczuk, and Saket Saurabh. Parameterized algorithms. Springer International Publishing, 2015. URL: https://doi.org/10.1007/978-3-319-21275-3.
  7. Reinhard Diestel. Graph Theory. Springer Publishing Company, Incorporated, 5th edition, 2017. Google Scholar
  8. Robert Elsässer and Tobias Tscheuschner. Settling the complexity of local max-cut (almost) completely. In International Colloquium on Automata, Languages, and Programming, pages 171-182. Springer, 2011. URL: https://doi.org/10.1007/978-3-642-22006-7_15.
  9. Armin Haken and Michael Luby. Steepest descent can take exponential time for symmetric connection networks. Complex Syst., 2(2):191-196, April 1988. URL: http://www.complex-systems.com/abstracts/v02_i02_a03.html.
  10. Peter L Hammer, Bruno Simeone, Th M Liebling, and Dominique de Werra. From linear separability to unimodality: A hierarchy of pseudo-boolean functions. SIAM Journal on Discrete Mathematics, 1(2):174-184, 1988. URL: https://doi.org/10.1137/0401019.
  11. David S. Johnson, Christos H. Papadimitriou, and Mihalis Yannakakis. How easy is local search? Journal of Computer and System Sciences, 37(1):79-100, 1988. URL: https://doi.org/10.1016/0022-0000(88)90046-3.
  12. Artem Kaznatcheev. Computational complexity as an ultimate constraint on evolution. Genetics, 212(1):245-265, 2019. URL: https://doi.org/10.1534/genetics.119.302000.
  13. Artem Kaznatcheev. Algorithmic Biology of Evolution and Ecology. PhD thesis, University of Oxford, 2020. Google Scholar
  14. Artem Kaznatcheev, David A Cohen, and Peter Jeavons. Representing fitness landscapes by valued constraints to understand the complexity of local search. Journal of Artificial Intelligence Research, 69:1077-1102, 2020. URL: https://doi.org/10.1613/jair.1.12156.
  15. Artem Kaznatcheev and Melle van Marle. Exponential steepest ascent from valued constraint graphs of pathwidth four. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024), pages 17:1-17:16, 2024. URL: https://doi.org/10.4230/LIPIcs.CP.2024.17.
  16. Artem Kaznatcheev and Sofia Vazquez Alferez. When is local search both effective and efficient?, 2024. URL: https://doi.org/10.48550/arXiv.2410.02634.
  17. Burkhard Monien and Tobias Tscheuschner. On the power of nodes of degree four in the local max-cut problem. In Algorithms and Complexity: 7th International Conference, CIAC 2010, Rome, Italy, May 26-28, 2010. Proceedings 7, pages 264-275. Springer, 2010. URL: https://doi.org/10.1007/978-3-642-13073-1_24.
  18. Svatopluk Poljak. Integer linear programs and local search for max-cut. SIAM Journal on Computing, 24(4):822-839, 1995. URL: https://doi.org/10.1137/S0097539793245350.
  19. Ingo A Schurr. Unique sink orientations of cubes. PhD thesis, ETH Zurich, 2004. Google Scholar
  20. Tibor Szabó and Emo Welzl. Unique sink orientations of cubes. In Proceedings 42nd IEEE Symposium on Foundations of Computer Science, pages 547-555. IEEE, 2001. URL: https://doi.org/10.1109/SFCS.2001.959931.
  21. Melle van Marle. Complexity of greedy local search for constraint satisfaction. Master’s thesis, Utrecht University, 2025. Google Scholar
  22. David P. Williamson and David B. Shmoys. Greedy Algorithms and Local Search, pages 27-56. Cambridge University Press, 2011. Google Scholar
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