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On robust vs fast solving of qualitative constraints

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Abstract

Qualitative Constraint Networks (\(\textsf{QCN}\)s) comprise a Symbolic AI framework for representing and reasoning about spatial and temporal information via the use of natural disjunctive qualitative relations, e.g., a constraint can be of the form “Task A is scheduled after or during Task C”. In qualitative constraint-based reasoning, the state-of-the-art approach to tackle a given \(\textsf{QCN}\) consists in employing a backtracking algorithm, where the branching decisions during search and the refinement of the \(\textsf{QCN}\) are governed by certain heuristics that have been proposed in the literature. Although there has been plenty of research on how these heuristics compare and behave in terms of checking the satisfiability of a \(\textsf{QCN}\) fast, to the best of our knowledge there has not been any study on how they compare and behave in terms of obtaining a tractable refinement of a \(\textsf{QCN}\) that is also robust. In brief, a robust refinement of a \(\textsf{QCN}\) can be primarily seen as one that retains as many qualitative solutions as possible, e.g., the configuration “Task A is scheduled after or during Task C” is more robust than “Task A is scheduled after Task C”. Here, we make such a preliminary comparison and evaluation with respect to prominent heuristics in the literature, and reveal that there exists a trade-off between fast and robust solving of \(\textsf{QCN}\)s for datasets consisting of instances of Allen’s Interval Algebra and Region Connection Calculus. Furthermore, we investigate reasons for the existence of this trade-off and find that more aggressive heuristics are more efficient at the cost of producing less robust refinements.

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Notes

  1. Note that the perturbation is applied to \(\mathcal {N}\), not to its refinement: \(\mathcal {N}^\prime \); thus, it is possible that the removed base relation \(b \in C(v,v^\prime )\) does not belong to \(C^\prime (v,v^\prime )\), viz., \(b \not \in C^\prime (v,v^\prime )\) (in this case, \(\mathcal {N}\) would not be affected by the perturbation).

  2. A sequence of perturbations describes a series of perturbations applied to \(\mathcal {N}\) one after the other.

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Authors and Affiliations

  1. Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, Netherlands

    Jan Wehner

  2. LIRMM UMR 5506, CNRS, University of Montpellier, Montpellier, France

    Michael Sioutis

  3. Faculty of Information Systems and Applied Computer Sciences, University of Bamberg, Bamberg, Germany

    Diedrich Wolter

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  1. Jan Wehner
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  2. Michael Sioutis
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  3. Diedrich Wolter
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Correspondence to Jan Wehner.

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Wehner, J., Sioutis, M. & Wolter, D. On robust vs fast solving of qualitative constraints. J Heuristics 29, 461–485 (2023). https://doi.org/10.1007/s10732-023-09517-8

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