Document Open Access Logo

Positive and Negative Length-Bound Reachability Constraints

Authors Luis Quesada , Kenneth N. Brown

PDF
Thumbnail PDF

File

LIPIcs.CP.2021.46.pdf
  • Filesize: 1.3 MB
  • 16 pages

Document Identifiers

Author Details

Luis Quesada
  • Insight Centre for Data Analytics, School of Computer Science, University College Cork, Ireland
Kenneth N. Brown
  • Insight Centre for Data Analytics, School of Computer Science, University College Cork, Ireland

Funding

This publication has emanated from research conducted with the financial support of Science Foundation Ireland under grant numbers 16/SP/3804 and 12/RC/2289-P2, which are co-funded under the European Regional Development Fund.

Acknowledgements

We thank Seán Óg Murphy, Liam O'Toole and Cormac J. Sreenan for initial discussions on the application that motivated this research, and Jaime Arias for sharing his experience with Visual Studio Code. Finally, we thank the anonymous referees for their help in improving the paper.

Cite As Get BibTex

Luis Quesada and Kenneth N. Brown. Positive and Negative Length-Bound Reachability Constraints. In 27th International Conference on Principles and Practice of Constraint Programming (CP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 210, pp. 46:1-46:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.CP.2021.46

Abstract

In many application problems, including physical security and wildlife conservation, infrastructure must be configured to ensure or deny paths between specified locations. We model the problem as sub-graph design subject to constraints on paths and path lengths, and propose length-bound reachability constraints. Although reachability in graphs has been modelled before in constraint programming, the interaction of positive and negative reachability has not been studied in depth. We prove that deciding whether a set of positive and negative reachability constraints are satisfiable is NP complete. We show the effectiveness of our approach on decision problems, and also on optimisation problems. We compare our approach with existing constraint models, and we demonstrate significant improvements in runtime and solution costs, on a new problem set.

Subject Classification

ACM Subject Classification
  • Theory of computation → Constraint and logic programming
Keywords
  • Reachability Constraints
  • Graph Connectivity
  • Constraint Programming

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Christian Bessiere, Emmanuel Hebrard, George Katsirelos, and Toby Walsh. Reasoning about connectivity constraints. In Qiang Yang and Michael J. Wooldridge, editors, Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, Buenos Aires, Argentina, July 25-31, 2015, pages 2568-2574. AAAI Press, 2015. URL: http://ijcai.org/Abstract/15/364.
  2. Geoffrey Chu. Improving combinatorial optimization. PhD thesis, University of Melbourne, Australia, 2011. URL: http://hdl.handle.net/11343/36679.
  3. Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms, Third Edition. The MIT Press, 3rd edition, 2009. Google Scholar
  4. Diego de Uña. Discrete optimization over graph problems. PhD thesis, University of Melbourne, Parkville, Victoria, Australia, 2018. URL: http://hdl.handle.net/11343/217321.
  5. Diego de Uña, Graeme Gange, Peter Schachte, and Peter J. Stuckey. A bounded path propagator on directed graphs. In Michel Rueher, editor, Principles and Practice of Constraint Programming - 22nd International Conference, CP 2016, Toulouse, France, September 5-9, 2016, Proceedings, volume 9892 of Lecture Notes in Computer Science, pages 189-206. Springer, 2016. URL: https://doi.org/10.1007/978-3-319-44953-1_13.
  6. Bistra Dilkina and Carla P. Gomes. Solving connected subgraph problems in wildlife conservation. In Andrea Lodi, Michela Milano, and Paolo Toth, editors, Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 7th International Conference, CPAIOR 2010, Bologna, Italy, June 14-18, 2010. Proceedings, volume 6140 of Lecture Notes in Computer Science, pages 102-116. Springer, 2010. URL: https://doi.org/10.1007/978-3-642-13520-0_14.
  7. Grégoire Dooms. The CP(Graph) computation domain in constraint programming. PhD thesis, Catholic University of Louvain, Louvain-la-Neuve, Belgium, 2006. URL: http://hdl.handle.net/2078.1/107275.
  8. Jean-Guillaume Fages and Xavier Lorca. Revisiting the tree constraint. In Jimmy Ho-Man Lee, editor, Principles and Practice of Constraint Programming - CP 2011 - 17th International Conference, CP 2011, Perugia, Italy, September 12-16, 2011. Proceedings, volume 6876 of Lecture Notes in Computer Science, pages 271-285. Springer, 2011. URL: https://doi.org/10.1007/978-3-642-23786-7_22.
  9. Department for Communities and Local Government. Fire safety risk assessment: offices and shops. The Stationery Office, UK, 2006. Google Scholar
  10. Markus Friedrich. Functional structuring of road networks. Transportation Research Procedia, 25:568-581, 2017. World Conference on Transport Research - WCTR 2016 Shanghai. 10-15 July 2016. URL: https://doi.org/10.1016/j.trpro.2017.05.439.
  11. M.L. Garcia. Design and Evaluation of Physical Protection Systems. Elsevier Science, 2007. Google Scholar
  12. M. R. Garey and David S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, 1979. Google Scholar
  13. Gecode Team. Gecode: Generic constraint development environment, 2019. Available from http://www.gecode.org. Google Scholar
  14. Alireza Karduni, Amirhassan Kermanshah, and Sybil Derrible. A protocol to convert spatial polyline data to network formats and applications to world urban road networks. Scientific Data, 3(1):160046, 2016. URL: https://doi.org/10.1038/sdata.2016.46.
  15. Petr Kolman and Ondrej Pangrác. On the complexity of paths avoiding forbidden pairs. Discret. Appl. Math., 157(13):2871-2876, 2009. URL: https://doi.org/10.1016/j.dam.2009.03.018.
  16. Seán Óg Murphy, Liam O'Toole, Luis Quesada, Kenneth N. Brown, and Cormac J. Sreenan. Ambient access control for smart spaces: dynamic guidance and zone configuration. In The 12th International Conference on Ambient Systems, Networks and Technologies (ANT), March 23-26, 2021, Warsaw, Poland, pages 330-337, 2021. Google Scholar
  17. Nicholas Nethercote, Peter J. Stuckey, Ralph Becket, Sebastian Brand, Gregory J. Duck, and Guido Tack. Minizinc: Towards a standard CP modelling language. In Principles and Practice of Constraint Programming - CP 2007, 13th International Conference, CP 2007, Providence, RI, USA, September 23-27, 2007, Proceedings, volume 4741, pages 529-543. Springer, 2007. URL: https://doi.org/10.1007/978-3-540-74970-7_38.
  18. The pandas development team. pandas-dev/pandas: Pandas, 2020. URL: https://doi.org/10.5281/zenodo.3509134.
  19. Liliana Pasquale, Carlo Ghezzi, Edoardo Pasi, Christos Tsigkanos, Menouer Boubekeur, Blanca Florentino-Liaño, Tarik Hadzic, and Bashar Nuseibeh. Topology-aware access control of smart spaces. Computer, 50(7):54-63, 2017. Google Scholar
  20. Luis Quesada. Solving Constrained Graph Problems using Reachability Constraints based on Transitive Closure and Dominators. PhD thesis, Catholic University of Louvain, Louvain-la-Neuve, Belgium, 2006. Google Scholar
  21. Luis Quesada, Peter Van Roy, Yves Deville, and Raphaël Collet. Using dominators for solving constrained path problems. In Pascal Van Hentenryck, editor, Practical Aspects of Declarative Languages, 8th International Symposium, PADL 2006, Charleston, SC, USA, January 9-10, 2006, Proceedings, volume 3819 of Lecture Notes in Computer Science, pages 73-87. Springer, 2006. URL: https://doi.org/10.1007/11603023_6.
  22. Meinolf Sellmann. Cost-based filtering for shorter path constraints. In Francesca Rossi, editor, Principles and Practice of Constraint Programming - CP 2003, 9th International Conference, CP 2003, Kinsale, Ireland, September 29 - October 3, 2003, Proceedings, volume 2833 of Lecture Notes in Computer Science, pages 694-708. Springer, 2003. URL: https://doi.org/10.1007/978-3-540-45193-8_47.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact