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

Finite Domain Bounds Consistency Revisited

A widely adopted approach to solving constraint satisfaction problems combines systematic tree search with constraint propagation for pruning the search space. Constraint propagation is performed by propagators implementing a certain notion of consistency. Bounds consistency is the method of choice for building propagators for arithmetic constraints and several global constraints in the finite integer domain. However, there has been some confusion in the definition of bounds consistency. In this paper we clarify the differences and similarities among the three commonly used notions of bounds consistency.Comment: 12 page

Local consistency for extended CSPs

AbstractWe extend the framework of Constraint Satisfaction Problems to make it more suitable for/applicable to modern constraint programming languages where both constraint satisfaction and constraint solving have a role. Some rough principles for local consistency conditions in the extended framework are developed, appropriate notions of local consistency are formulated, and relationships between the various consistency conditions are established

A Framework for Decision-based Consistencies

International audienceConsistencies are properties of constraint networks that can be enforced by appropriate algorithms to reduce the size of the search space to be explored. Recently, many consistencies built upon taking decisions (most often, variable assignments) and stronger than (general- ized) arc consistency have been introduced. In this paper, our ambition is to present a clear picture of decision-based consistencies. We identify four general classes (or levels) of decision-based consistencies, denoted by S∆φ, E∆φ, B∆φ and D∆φ, study their relationships, and show that known consistencies are particular cases of these classes. Interestingly, this gen- eral framework provides us with a better insight into decision-based con- sistencies, and allows us to derive many new consistencies that can be directly integrated and compared with other ones

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