A Microstructure-based Family of Tractable Classes for CSPs

Abstract : The study of tractable classes is an important issue in Artificial Intelligence, especially in Constraint Satisfaction Problems. In this context, the Broken Triangle Property (BTP) is a state-of-the-art microstructure-based tractable class which generalizes well-known and previously-defined tractable classes, notably the set of instances whose constraint graph is a tree. In this paper, we propose to extend and to generalize this class using a more general approach based on a parameter k which is a given constant. To this end, we introduce the k-BTP property (and the class of instances satisfying this property) such that we have 2-BTP = BTP, and for k > 2, k-BTP is a relaxation of BTP in the sense that k-BTP is a subset of (k + 1)-BTP. Moreover, we show that if k-TW is the class of instances having tree-width bounded by a constant k, then k-TW is a subset of (k + 1)-BTP. Concerning tractability, we show that instances satisfying k-BTP and which are strong k-consistent are tractable, that is, can be recognized and solved in polynomial time. We also study the relationship between k-BTP and the approach of Naanaa who proposed a set-theoretical tool, known as the directional rank, to extend tractable classes in a parameterized way. Finally we propose an experimental study of 3-BTP which shows the practical interest of this class, particularly w.r.t. the practical solving of instances satisfying 3-BTP and for other instances, w.r.t. to backdoors based on this tractable class.
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  • HAL Id : hal-01343050, version 1
  • OATAO : 15358

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Martin Cooper, Philippe Jégou, Cyril Terrioux. A Microstructure-based Family of Tractable Classes for CSPs. 21st International Conference on Principles and Practice of Constraint Programming (CP 2015), Aug 2015, Cork, Ireland. pp. 74-88. ⟨hal-01343050⟩

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