Combinatorial Search

  • Vladimir Lifschitz


In a combinatorial search problem, the goal is to find a solution among a finite number of candidates. The ASP approach is to encode such a problem as a logic program whose stable models correspond to solutions, and then use an answer set solver to find a stable model.


  1. 3.
    Markus Aschinger, Conrad Drescher, Gerhard Friedrich, Georg Gottlob, Peter Jeavons, Anna Ryabokon, and Evgenij Thorstensen. Optimization methods for the partner units problem. In Proceedings of the Eigth International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, pages 4–19, 2011.Google Scholar
  2. 12.
    Leonard Baumert and Solomon Golomb. Backtrack programming. Journal of the ACM, 12:516–524, 1965.MathSciNetCrossRefGoogle Scholar
  3. 18.
    Marco Calautti, Sergio Greco, and Irina Trubitsyna. Detecting decidable classes of finitely ground logic programs with function symbols. ACM Transactions on Computational Logic, 18(4):28:1–28:42, November 2017.Google Scholar
  4. 19.
    Francesco Calimeri, Susanna Cozza, Giovambattista Ianni, and Nicola Leone. Computable functions in ASP: theory and implementation. In Proceedings of International Conference on Logic Programming (ICLP), pages 407–424, 2008.Google Scholar
  5. 23.
    Vas̆ek Chvátal. Some unknown van der Waerden numbers. In Richard Guy, Haim Hanani, and Norbert Sauer, editors, Combinatorial Structures and Their Applications, pages 31–33. New York: Gordon and Breach, 2009.Google Scholar
  6. 41.
    Raphael Finkel, Wiktor Marek, and Miroslaw Truszczynski. Constraint Lingo: towards high-level constraint programming. Software: Practice and Experience, 34(15):1481–1504, 2004.Google Scholar
  7. 43.
    Harold Fredricksen and Melvin Sweet. Symmetric sum-free partitions and lower bounds for Schur numbers. Electronic Journal of Combinatorics, 7, 2000.Google Scholar
  8. 65.
    Marijn Heule. Schur number five. In Proceedings of AAAI Conference on Artificial Intelligence, 2018.Google Scholar
  9. 69.
    Richard Karp. Reducibility among combinatorial problems. In R. E. Miller and J. W. Thatcher, editors, Complexity of Computer Computations, pages 85–103. Plenum, 1972.Google Scholar
  10. 71.
    Daniel Korman, Erik Mack, Jacob Jett, and Allen Renear. Defining textual entailment. Journal of the Association for Information Science and Technology, 69(6):763–772, 2018.CrossRefGoogle Scholar
  11. 72.
    Michal Kouril. Computing the van der Waerden number W(3,4)=293. Integers, 2012.Google Scholar
  12. 77.
    Yuliya Lierler and Vladimir Lifschitz. One more decidable class of finitely ground programs. In Proceedings of International Conference on Logic Programming (ICLP), 2009.Google Scholar
  13. 78.
    Yuliya Lierler and Vladimir Lifschitz. Termination of grounding is not preserved by strongly equivalent transformations. In Procedings of International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR), 2011.Google Scholar
  14. 95.
    Arindal Mitra and Chitta Baral. Learning to automatically solve logic grid puzzles. In Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing, pages 1023–1033, 2015.Google Scholar
  15. 109.
    Issai Schur. Über die Kongruenz x m + y m ≡ z m (mod p). Jahresbericht der Deutschen Mathematiker-Vereinigung, 25:114–116, 1916.zbMATHGoogle Scholar
  16. 110.
    Rolf Schwitter. The jobs puzzle: Taking on the challenge via controlled natural language processing. Theory and Practice of Logic Programming, 13(4,5):487–501, 2013.Google Scholar
  17. 117.
    Bartel Leendert van der Waerden. Beweis einer Baudetschen Vermutung. Nieuw Archief voor Wiskunde, 15:212–216, 1927.Google Scholar
  18. 119.
    Niklaus Wirth. Algorithms + Data Structures = Programs. Prentice Hall, 1976.Google Scholar
  19. 121.
    Larry Wos, Ross Overbeek, Ewing Lusk, and Jim Boyle. Automated Reasoning: Introduction and Applications. Prentice Hall, 1984.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Vladimir Lifschitz
    • 1
  1. 1.Department of Computer ScienceUniversity of Texas at AustinAustinUSA

Personalised recommendations