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Dynamic Branching in Qualitative Constraint Networks via Counting Local Models

Authors Michael Sioutis , Diedrich Wolter

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Michael Sioutis
  • Faculty of Information Systems and Applied Computer Sciences, University of Bamberg, Germany
Diedrich Wolter
  • Faculty of Information Systems and Applied Computer Sciences, University of Bamberg, Germany

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Michael Sioutis and Diedrich Wolter. Dynamic Branching in Qualitative Constraint Networks via Counting Local Models. In 27th International Symposium on Temporal Representation and Reasoning (TIME 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 178, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.TIME.2020.12

Abstract

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

Subject Classification

ACM Subject Classification
  • Theory of computation → Constraint and logic programming
  • Computing methodologies → Temporal reasoning
  • Computing methodologies → Spatial and physical reasoning
Keywords
  • Qualitative constraints
  • spatial and temporal reasoning
  • counting local models
  • dynamic branching
  • adaptive algorithm

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