A Lazy Algorithm to Efficiently Approximate Singleton Path Consistency for Qualitative Constraint Networks

Abstract

Partial singleton (weak) path consistency, or partial ♦-consistency, for a qualitative constraint network, ensures that the process of instantiating any constraint of that network with any of its base relations b and enforcing partial (weak) path consistency, or partial ⋄-consistency, in the updated network, yields a partially ⋄-consistent subnetwork where the respective constraint is still defined by b. This local consistency is essential for helping to decide the satisfiability of challenging qualitative constraint networks and has been shown to play a crucial role in tackling more demanding problems associated with a given qualitative constraint network, such as the problem of minimal labeling. One of the main downsides to using partial ♦-consistency, is that it is computationally expensive to enforce in a given qualitative constraint network, as, despite being a local consistency in principle, it retains a global scope of the network at hand. In this paper, we propose a lazy algorithm that restricts the singleton checks associated with partial ♦-consistency to constraints that are likely to lead to the removal of a base relation upon their propagation. A key feature of this algorithm is that it collectively eliminates certain unfeasible base relations by exploiting singleton checks. Further, we show that the closure that is obtained by our algorithm is incomparable to the one that is entailed by partial ♦-consistency and non-unique in general. We demonstrate the efficiency of our algorithm via an experimental evaluation with random Interval Algebra networks from the phase transition region of two separate models and, moreover, show that it can exhibit very similar pruning capability for such networks to the one of an algorithm for enforcing partial ♦-consistency.