On the Efficiency of Backtracking Algorithms for Binary Constraint Satisfaction Problems

Achref El Mouelhi 1 Philippe Jegou 1 Cyril Terrioux 1 Bruno Zanuttini 2
2 Equipe MAD - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : The question of tractable classes of constraint satisfaction problems (CSPs) has been studied for a long time, and is now a very active research domain. However, studies of tractable classes are typically very theoretical. They usually introduce classes of instances together with polynomial time algorithms for recognizing and solving them, and the algorithms can be used only for the new class. In this paper, we address the issue of tractable classes of CSPs from a different perspective. We investigate the complexity of classical, generic algorithms for solving CSPs (such as Forward Checking). We introduce a new parameter for measuring their complexity and derive new complexity bounds. By relating the complexity of CSP algorithms to graph-theoretic parameters, our analysis allows us to point at new tractable classes, which can be solved directly by the usual CSP algorithms in polynomial time, and without the need to recognize the classes in advance.
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Achref El Mouelhi, Philippe Jegou, Cyril Terrioux, Bruno Zanuttini. On the Efficiency of Backtracking Algorithms for Binary Constraint Satisfaction Problems. Proc. International Symposium on Artificial Intelligence and Mathematics (ISAIM 2012), Jan 2012, United States. 7 p. ⟨hal-00946876⟩

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