Skip to main content
SpringerLink
Log in

Combinatorial Search

  • Chapter
  • First Online:
Answer Set Programming

  • 2074 Accesses

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 64.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. 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. Leonard Baumert and Solomon Golomb. Backtrack programming. Journal of the ACM, 12:516–524, 1965.

    Article  MathSciNet  Google Scholar 

  3. 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. 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. 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. 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. Harold Fredricksen and Melvin Sweet. Symmetric sum-free partitions and lower bounds for Schur numbers. Electronic Journal of Combinatorics, 7, 2000.

    Google Scholar 

  8. Marijn Heule. Schur number five. In Proceedings of AAAI Conference on Artificial Intelligence, 2018.

    Google Scholar 

  9. 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. 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.

    Article  Google Scholar 

  11. Michal Kouril. Computing the van der Waerden number W(3,4)=293. Integers, 2012.

    Google Scholar 

  12. 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. 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. 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. Issai Schur. Über die Kongruenz x m + y m ≡ z m (mod p). Jahresbericht der Deutschen Mathematiker-Vereinigung, 25:114–116, 1916.

    MATH  Google Scholar 

  16. 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. Bartel Leendert van der Waerden. Beweis einer Baudetschen Vermutung. Nieuw Archief voor Wiskunde, 15:212–216, 1927.

    Google Scholar 

  18. Niklaus Wirth. Algorithms + Data Structures = Programs. Prentice Hall, 1976.

    Google Scholar 

  19. Larry Wos, Ross Overbeek, Ewing Lusk, and Jim Boyle. Automated Reasoning: Introduction and Applications. Prentice Hall, 1984.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Texas at Austin, Austin, TX, USA

    Vladimir Lifschitz

Authors
  1. Vladimir Lifschitz
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Lifschitz, V. (2019). Combinatorial Search. In: Answer Set Programming. Springer, Cham. https://doi.org/10.1007/978-3-030-24658-7_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-24658-7_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-24657-0

  • Online ISBN: 978-3-030-24658-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation