About the choice of the variable to unassign in a decision repair algorithm

The decision repair algorithm, which has been designed to solve constraint satisfaction problems (CSP), can be seen, either (i) as an extension of the classical depth first tree search algorithm with the introduction of a free choice of the variable to which to backtrack in case of inconsistency, or (ii) as a local search algorithm in the space of the partial consistent variable assignments, or (iii) as a hybridisation between local search and constraint propagation. Experiments reported by Pralet and Verfaillie show that some heuristics for the choice of the variable to which to backtrack behave well on consistent instances and that other heuristics behave well on inconsistent ones. They show also that, despite its a priori incompleteness, decision repair, equipped with some specific heuristics, can solve within a limited time almost all the consistent and inconsistent randomly generated instances over the whole constrainedness spectrum. In this paper, we discuss the heuristics that could be used by decision repair to solve consistent instances, on the one hand, and inconsistent ones, on the other hand. Moreover, we establish that some specific heuristics make decision repair complete.