Hidden Tractable Classes: From Theory to Practice

Tractable classes constitute an important issue in CP, at least from a theoretical viewpoint. But they are not actually used in practice. Either their treatment is too costly for time complexity or, even if there exist efficient algorithms to manage them, they do not appear in the real problems. We propose here to address this issue thanks to the notion of hidden tractable classes. Such classes are based on a known tractable class C, and a transformation t, and are defined by sets of instances P such that their transformation using t is in C, that is t (P) in C. We propose a general framework to study such notions. After, we focus our study on the tractable class BTP, and several transformations which are the filterings classically used in CP. We show then that the use of filterings allows sometimes to highlight the occurrence of BTP in the benchmarks generally considered for solver comparisons, i.e. That BTP is sometimes "hidden" in the benchmarks. Thus, this approach allows to extend the set of known tractable classes.