Skip to main content
Springer Nature Link
Log in

Proof Logging for the Circuit Constraint

  • Conference paper
  • First Online:
Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14743))

  • 458 Accesses

Abstract

Proof logging in constraint programming is an approach to certifying a conclusion reached by a solver. To allow for this, different propagators must be augmented to produce justifications for any inferences they make, so that an independent proof checker can certify correctness. The Circuit constraint is used to enforce a Hamiltonian cycle on a set of vertices, e.g. for vehicle routing. Maintaining consistency for the Circuit constraint is hard, so various ad-hoc propagation techniques have been devised and implemented in solvers. We show that standard Circuit constraint inference rules can be efficiently justified within a pseudo-Boolean proof system, either by using a simple sequence of cutting planes steps or through a conditional counting argument.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    https://zenodo.org/records/10848992.

References

  1. Berg, J., Bogaerts, B., Nordström, J., Oertel, A., Vandesande, D.: Certified core-guided MaxSAT solving. In: Pientka, B., Tinelli, C. (eds.) CADE 2023. LNCS, vol. 14132, pp. 1–22. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-38499-8_1

    Chapter  Google Scholar 

  2. Bogaerts, B., Gocht, S., McCreesh, C., Nordström, J.: Certified symmetry and dominance breaking for combinatorial optimisation. J. Artif. Intell. Res. 77, 1539–1589 (2023). Preliminary version in AAAI 2022

    Google Scholar 

  3. Buss, S.R., Nordström, J.: Proof complexity and SAT solving. In: Biere, A., Heule, M.J.H., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, vol. 336, chap. 7, 2nd edn., pp. 233–350. IOS Press (2021)

    Google Scholar 

  4. Caseau, Y., Laburthe, F.: Solving small TSPs with constraints. In: Naish, L. (ed.) Logic Programming, Proceedings of the Fourteenth International Conference on Logic Programming, Leuven, Belgium, 8–11 July 1997, pp. 316–330. MIT Press (1997)

    Google Scholar 

  5. Cheung, K.K.H., Gleixner, A., Steffy, D.E.: Verifying integer programming results. In: Eisenbrand, F., Koenemann, J. (eds.) IPCO 2017. LNCS, vol. 10328, pp. 148–160. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59250-3_13

    Chapter  Google Scholar 

  6. Chu, G., Stuckey, P.J., Schutt, A., Ehlers, T., Gange, G., Francis, K.: Chuffed, a lazy clause generation solver (2023). https://github.com/chuffed/chuffed

  7. Cook, W., Coullard, C.R., Turán, Gy.: On the complexity of cutting-plane proofs. Discrete Appl. Math. 18(1), 25–38 (1987). https://doi.org/10.1016/0166-218X(87)90039-4

  8. Cruz-Filipe, L., Heule, M.J.H., Hunt, W.A., Kaufmann, M., Schneider-Kamp, P.: Efficient certified RAT verification. In: de Moura, L. (ed.) CADE 2017. LNCS (LNAI), vol. 10395, pp. 220–236. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63046-5_14

    Chapter  Google Scholar 

  9. Di Gaspero, L., Urli, T.: A CP/LNS approach for multi-day homecare scheduling problems. In: Blesa, M.J., Blum, C., Voß, S. (eds.) HM 2014. LNCS, vol. 8457, pp. 1–15. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-07644-7_1

    Chapter  Google Scholar 

  10. Elffers, J., Gocht, S., McCreesh, C., Nordström, J.: Justifying all differences using pseudo-boolean reasoning. In: The Thirty-Fourth AAAI Conference on Artificial Intelligence, AAAI 2020, The Thirty-Second Innovative Applications of Artificial Intelligence Conference, IAAI 2020, The Tenth AAAI Symposium on Educational Advances in Artificial Intelligence, EAAI 2020, New York, NY, USA, 7–12 February 2020, pp. 1486–1494. AAAI Press (2020)

    Google Scholar 

  11. Fages, J.G., Lorca, X.: Improving the asymmetric TSP by considering graph structure (2012). https://doi.org/10.48550/arXiv.1206.3437

  12. Francis, K.G., Stuckey, P.J.: Explaining circuit propagation. Constraints 19(1), 1–29 (2014). https://doi.org/10.1007/s10601-013-9148-0

    Article  MathSciNet  Google Scholar 

  13. Gaspero, L.D., Rendl, A., Urli, T.: Balancing bike sharing systems with constraint programming. Constraints 21(2), 318–348 (2016). https://doi.org/10.1007/s10601-015-9182-1

    Article  MathSciNet  Google Scholar 

  14. Gecode Team: Gecode: generic constraint development environment (2023). http://www.gecode.org

  15. Gocht, S.: Certifying correctness for combinatorial algorithms: by using pseudo-Boolean reasoning. Ph.D. thesis, Lund University, Sweden (2022)

    Google Scholar 

  16. Gocht, S., McCreesh, C., Nordström, J.: An auditable constraint programming solver. In: Solnon, C. (ed.) Proceeding of the 28th International Conference on Principles and Practice of Constraint Programming. Leibniz International Proceedings in Informatics (LIPIcs), vol. 235, pp. 25:1–25:18. Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl (2022). https://doi.org/10.4230/LIPIcs.CP.2022.25

  17. Heule, M.J.H.: Chinese remainder encoding for Hamiltonian cycles. In: Li, C.-M., Manyà, F. (eds.) SAT 2021. LNCS, vol. 12831, pp. 216–224. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-80223-3_15

    Chapter  Google Scholar 

  18. Italiano, G.F., Laura, L., Santaroni, F.: Finding strong bridges and strong articulation points in linear time. Theoret. Comput. Sci. 447, 74–84 (2012). https://doi.org/10.1016/j.tcs.2011.11.011

    Article  MathSciNet  Google Scholar 

  19. Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W., Bohlinger, J.D. (eds.) Complexity of Computer Computations. The IBM Research Symposia Series, pp. 85–103. Springer, Boston (1972). https://doi.org/10.1007/978-1-4684-2001-2_9

    Chapter  Google Scholar 

  20. Kraiczy, S., McCreesh, C.: Solving graph homomorphism and subgraph isomorphism problems faster through clique neighbourhood constraints. In: Zhou, Z. (ed.) Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence, IJCAI 2021, Virtual Event/Montreal, Canada, 19–27 August 2021, pp. 1396–1402. ijcai.org (2021). https://doi.org/10.24963/IJCAI.2021/193

  21. Kuchcinski, K., Szymanek, R.: JaCoP - Java constraint programming solver. In: CP Solvers: Modeling, Applications, Integration, and Standardization, Co-located with the 19th International Conference on Principles and Practice of Constraint Programming (2013)

    Google Scholar 

  22. Lam, E., Van Hentenryck, P.: A branch-and-price-and-check model for the vehicle routing problem with location congestion. Constraints 21(3), 394–412 (2016). https://doi.org/10.1007/s10601-016-9241-2

    Article  MathSciNet  Google Scholar 

  23. Lam, E., Van Hentenryck, P., Kilby, P.: Joint vehicle and crew routing and scheduling. In: Pesant, G. (ed.) CP 2015. LNCS, vol. 9255, pp. 654–670. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23219-5_45

    Chapter  Google Scholar 

  24. McCreesh, C., McIlree, M.: The Glasgow constraint solver. GitHub repository (2023). https://github.com/ciaranm/glasgow-constraint-solver

  25. McIlree, M.J., McCreesh, C.: Proof logging for smart extensional constraints. In: Yap, R.H.C. (ed.) 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), vol. 280, pp. 26:1–26:17. Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl (2023). https://doi.org/10.4230/LIPIcs.CP.2023.26

  26. Michel, L.D., Schaus, P., Van Hentenryck, P.: MiniCP: a lightweight solver for constraint programming. Math. Program. Comput. 13(1), 133–184 (2021). https://doi.org/10.1007/s12532-020-00190-7

    Article  MathSciNet  Google Scholar 

  27. Ohrimenko, O., Stuckey, P.J., Codish, M.: Propagation = lazy clause generation. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 544–558. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74970-7_39

    Chapter  Google Scholar 

  28. Perron, L., Didier, F.: CP-SAT. https://developers.google.com/optimization/cp/cp_solver/

  29. Pesant, G., Gendreau, M., Potvin, J.Y., Rousseau, J.M.: An exact constraint logic programming algorithm for the traveling salesman problem with time windows. Transp. Sci. 32(1), 12–29 (1998). https://doi.org/10.1287/trsc.32.1.12

    Article  Google Scholar 

  30. Schulte, C., Tack, G.: Weakly monotonic propagators. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 723–730. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04244-7_56

    Chapter  Google Scholar 

  31. Tarjan, R.: Depth-first search and linear graph algorithms. SIAM J. Comput. 1(2), 146–160 (1972). https://doi.org/10.1137/0201010

    Article  MathSciNet  Google Scholar 

  32. Wetzler, N., Heule, M.J.H., Hunt, W.A.: DRAT-trim: efficient checking and trimming using expressive clausal proofs. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 422–429. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_31

    Chapter  Google Scholar 

  33. Zhou, N.-F.: In pursuit of an efficient SAT encoding for the Hamiltonian cycle problem. In: Simonis, H. (ed.) CP 2020. LNCS, vol. 12333, pp. 585–602. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-58475-7_34

    Chapter  Google Scholar 

Download references

Acknowledgements

Ciaran McCreesh was supported by a Royal Academy of Engineering research fellowship, and by the Engineering and Physical Sciences Research Council [grant number EP/X030032/1]. Jakob Nordström was supported by the Swedish Research Council grant 2016-00782 and the Independent Research Fund Denmark grant 9040-00389B. For the purpose of open access, the authors have applied a creative commons attribution (CC BY) licence to any author accepted manuscript version arising from this work.

Author information

Authors and Affiliations

  1. University of Glasgow, Glasgow, Scotland

    Matthew J. McIlree & Ciaran McCreesh

  2. University of Copenhagen, Copenhagen, Denmark

    Jakob Nordström

  3. Lund University, Lund, Sweden

    Jakob Nordström

Authors
  1. Matthew J. McIlree
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ciaran McCreesh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jakob Nordström
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Matthew J. McIlree .

Editor information

Editors and Affiliations

  1. University of Southern California, Los Angeles, CA, USA

    Bistra Dilkina

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

McIlree, M.J., McCreesh, C., Nordström, J. (2024). Proof Logging for the Circuit Constraint. In: Dilkina, B. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2024. Lecture Notes in Computer Science, vol 14743. Springer, Cham. https://doi.org/10.1007/978-3-031-60599-4_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-60599-4_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-60601-4

  • Online ISBN: 978-3-031-60599-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics