On neighbourhood singleton-style consistencies for qualitative spatial and temporal reasoning

Given a qualitative constraint network (QCN), a singleton-style consistency focuses on each base relation (atom) of a constraint separately, rather than the entire constraint altogether. This local consistency is essential for tackling fundamental reasoning problems associated with QCNs, such as minimal labeling, but can suffer from redundant constraint checks, especially when checks occur far from where the pruning usually takes place. In this paper, we propose singleton-style consistencies that are applied just on the neighbourhood of a singleton-checked constraint instead of the whole network. We make a theoretical comparison with existing consistencies and consequently prove some properties of the new ones. Further, we propose algorithms to enforce our consistencies, as well as parsimonious variants thereof, that are more efficient in practice than the state of the art. An experimental evaluation with random and structured QCNs of Allen's Interval Algebra in the phase transition region demonstrates the potential of our approach.acceptedVersionPeer reviewe

Higher-Level Consistencies: Where, When, and How Much

Determining whether or not a Constraint Satisfaction Problem (CSP) has a solution is NP-complete. CSPs are solved by inference (i.e., enforcing consistency), conditioning (i.e., doing search), or, more commonly, by interleaving the two mechanisms. The most common consistency property enforced during search is Generalized Arc Consistency (GAC). In recent years, new algorithms that enforce consistency properties stronger than GAC have been proposed and shown to be necessary to solve difficult problem instances. We frame the question of balancing the cost and the pruning effectiveness of consistency algorithms as the question of determining where, when, and how much of a higher-level consistency to enforce during search. To answer the `where\u27 question, we exploit the topological structure of a problem instance and target high-level consistency where cycle structures appear. To answer the \u27when\u27 question, we propose a simple, reactive, and effective strategy that monitors the performance of backtrack search and triggers a higher-level consistency as search thrashes. Lastly, for the question of `how much,\u27 we monitor the amount of updates caused by propagation and interrupt the process before it reaches a fixpoint. Empirical evaluations on benchmark problems demonstrate the effectiveness of our strategies. Adviser: B.Y. Choueiry and C. Bessier

Higher-Level Consistencies: Where, When, and How Much

Determining whether or not a Constraint Satisfaction Problem (CSP) has a solution is NP-complete. CSPs are solved by inference (i.e., enforcing consistency), conditioning (i.e., doing search), or, more commonly, by interleaving the two mechanisms. The most common consistency property enforced during search is Generalized Arc Consistency (GAC). In recent years, new algorithms that enforce consistency properties stronger than GAC have been proposed and shown to be necessary to solve difficult problem instances. We frame the question of balancing the cost and the pruning effectiveness of consistency algorithms as the question of determining where, when, and how much of a higher-level consistency to enforce during search. To answer the `where\u27 question, we exploit the topological structure of a problem instance and target high-level consistency where cycle structures appear. To answer the \u27when\u27 question, we propose a simple, reactive, and effective strategy that monitors the performance of backtrack search and triggers a higher-level consistency as search thrashes. Lastly, for the question of `how much,\u27 we monitor the amount of updates caused by propagation and interrupt the process before it reaches a fixpoint. Empirical evaluations on benchmark problems demonstrate the effectiveness of our strategies. Adviser: B.Y. Choueiry and C. Bessier

Higher-Level Consistencies: Where, When, and How Much

Determining whether or not a Constraint Satisfaction Problem (CSP) has a solution is NP-complete. CSPs are solved by inference (i.e., enforcing consistency), conditioning (i.e., doing search), or, more commonly, by interleaving the two mechanisms. The most common consistency property enforced during search is Generalized Arc Consistency (GAC). In recent years, new algorithms that enforce consistency properties stronger than GAC have been proposed and shown to be necessary to solve difficult problem instances. We frame the question of balancing the cost and the pruning effectiveness of consistency algorithms as the question of determining where, when, and how much of a higher-level consistency to enforce during search. To answer the `where\u27 question, we exploit the topological structure of a problem instance and target high-level consistency where cycle structures appear. To answer the \u27when\u27 question, we propose a simple, reactive, and effective strategy that monitors the performance of backtrack search and triggers a higher-level consistency as search thrashes. Lastly, for the question of `how much,\u27 we monitor the amount of updates caused by propagation and interrupt the process before it reaches a fixpoint. Empirical evaluations on benchmark problems demonstrate the effectiveness of our strategies. Adviser: B.Y. Choueiry and C. Bessier

Adaptive Singleton-based Consistencies

International audienceSingleton-based consistencies have been shown to dra- matically improve the performance of constraint solvers on some difficult instances. However, they are in gen- eral too expensive to be applied exhaustively during the whole search. In this paper, we focus on partition-one- AC, a singleton-based consistency which, as opposed to singleton arc consistency, is able to prune values on all variables when it performs singleton tests on one of them. We propose adaptive variants of partition-one- AC that do not necessarily run until having proved the fixpoint. The pruning can be weaker than the full ver- sion but the computational effort can be significantly reduced. Our experiments show that adaptive Partition- one-AC can obtain significant speed-ups over arc con- sistency and over the full version of partition-one-AC

Adaptive Singleton-based Consistencies

International audienceSingleton-based consistencies have been shown to dra- matically improve the performance of constraint solvers on some difficult instances. However, they are in gen- eral too expensive to be applied exhaustively during the whole search. In this paper, we focus on partition-one- AC, a singleton-based consistency which, as opposed to singleton arc consistency, is able to prune values on all variables when it performs singleton tests on one of them. We propose adaptive variants of partition-one- AC that do not necessarily run until having proved the fixpoint. The pruning can be weaker than the full ver- sion but the computational effort can be significantly reduced. Our experiments show that adaptive Partition- one-AC can obtain significant speed-ups over arc con- sistency and over the full version of partition-one-AC