Positive and Negative Length-Bound Reachability Constraints

Authors Luis Quesada , Kenneth N. Brown

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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


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.

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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)


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
  • Reachability Constraints
  • Graph Connectivity
  • Constraint Programming


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