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 \(\subsetneq \) \((k+1)\)-BTP. Moreover, we show that if k-TW is the class of instances having tree-width bounded by a constant k, then k-TW \(\subsetneq \) \((k+1)\)-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.
Supported by ANR Project ANR-10-BLAN-0210 and EPSRC grant EP/L021226/1.
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Cooper, M.C., Jégou, P., Terrioux, C. (2015). A Microstructure-Based Family of Tractable Classes for CSPs. In: Pesant, G. (eds) Principles and Practice of Constraint Programming. CP 2015. Lecture Notes in Computer Science(), vol 9255. Springer, Cham. https://doi.org/10.1007/978-3-319-23219-5_6
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DOI: https://doi.org/10.1007/978-3-319-23219-5_6
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