Dynamic Branching in Qualitative Constraint Networks via Counting Local Models

Abstract

11 We introduce and evaluate dynamic branching strategies for solving Qualitative Constraint 12 Networks ( QCN s), which are networks that are mostly used to represent and reason about spatial 13 and temporal information via the use of simple qualitative relations, e.g., a constraint can be “Task A 14 is scheduled after or during Task C ”. In qualitative constraint-based reasoning, the state-of-the-art 15 approach to tackle a given QCN consists in employing a backtracking algorithm, where the branching 16 decisions during search are governed by the restrictiveness of the possible relations for a given 17 constraint (e.g., after can be more restrictive than during ). In the literature, that restrictiveness is 18 defined a priori by means of static weights that are precomputed and associated with the relations 19 of a given calculus, without any regard to the particulars of a given network instance of that 20 calculus, such as its structure. In this paper, we address this limitation by proposing heuristics that 21 dynamically associate a weight with a relation, based on the count of local models (or local scenarios ) 22 that the relation is involved with in a given QCN ; these models are local in that they focus on 23 triples of variables instead of the entire QCN . Therefore, our approach is adaptive and seeks to make 24 branching decisions that preserve most of the solutions by determining what proportion of local 25 solutions agree with that decision. Experimental results with a random and a structured dataset of 26 QCN s of Interval Algebra show that it is possible to achieve up to 5 times better performance for 27 structured instances, whilst maintaining non-negligible gains of around 20%