Plotting: A Planning Problem with Complex Transitions

Authors Joan Espasa , Ian Miguel , Mateu Villaret

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Author Details

Joan Espasa
  • School of Computer Science, University of St Andrews, UK
Ian Miguel
  • School of Computer Science, University of St Andrews, UK
Mateu Villaret
  • Department of Computer Science, Applied Mathematics and Statistics, University of Girona, Spain

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Joan Espasa, Ian Miguel, and Mateu Villaret. Plotting: A Planning Problem with Complex Transitions. In 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 235, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


We focus on a planning problem based on Plotting, a tile-matching puzzle video game published by Taito. The objective of the game is to remove at least a certain number of coloured blocks from a grid by sequentially shooting blocks into the same grid. The interest and difficulty of Plotting is due to the complex transitions after every shot: various blocks are affected directly, while others can be indirectly affected by gravity. We highlight the difficulties and inefficiencies of modelling and solving Plotting using PDDL, the de-facto standard language for AI planners. We also provide two constraint models that are able to capture the inherent complexities of the problem. In addition, we provide a set of benchmark instances, an instance generator and an extensive experimental comparison demonstrating solving performance with SAT, CP, MIP and a state-of-the-art AI planner.

Subject Classification

ACM Subject Classification
  • Theory of computation → Constraint and logic programming
  • Computing methodologies → Planning and scheduling
  • AI Planning
  • Modelling
  • Constraint Programming


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