Mind the gaps: A new splitting strategy for consistency techniques

Abstract

Classical methods for solving numerical CSPs are based on a branch and prune algorithm, a dichotomic enumeration process interleaved with a consistency filtering algorithm. In many interval solvers, the pruning step is based on local consistencies or partial consistencies. The associated pruning algorithms compute numerous data required to identify gaps within some domains, i.e. inconsistent intervals strictly included in the domain. However, these gaps are only used to compute the smallest approximation of the box enclosing all the solutions. This paper introduces a search strategy, named MindTheGaps, that takes advantage of the gaps identified during the filtering process. Gaps are collected with a negligible overhead, and are used to select the splitting direction as well as to define relevant cutting points within the domain. Splitting the domain by removing such gaps definitely reduces the search space. It also helps to discard some redundant solutions and helps the search algorithm to isolate different solutions. First experimental results show that MindTheGaps significantly improves performances of the search process. © Springer-Verlag Berlin Heidelberg 2005.