Papers by Berthe Y Choueiry
National Conference on Artificial Intelligence, Jul 1, 1998
In [4], Freuder defines several types of interchangeability to capture the equivalence among the ... more In [4], Freuder defines several types of interchangeability to capture the equivalence among the values of a variable in a discrete constraint satisfaction problem (CSP), and provides a procedure for computing one type of local interchangeability. In this paper, we first extend this procedure for computing a weak form of local interchangeability. Second, we show that the modified procedure can be used to generate a conjunctive decomposition of the CSP by localizing, in the CSP, independent subproblems. Third, for the case of constraints of mutual exclusion, we show that locally interchangeable values can be computed in a straightforward manner, and that the only possible type of local interchangeability is the one that induces locally independent subproblems. Finally, we give hints on how to exploit these results in practice, establish a lattice that relates some types of interchangeability, and identify directions for future research.
In this paper we propose a new efficient algorithm, the ¢ STP-solver, for computing the minimal n... more In this paper we propose a new efficient algorithm, the ¢ STP-solver, for computing the minimal network of the Simple Temporal Problem (STP). This algorithm achieves high performance by exploiting a topological property of the constraint graph (i.e., triangulation) and a semantic property of the constraints (i.e., convexity) in light of the results reported by Bliek and Sam-Haroud [1], which were presented for general CSPs and have not yet been applied to temporal networks. Importantly, we design the constraint propagation in ¢ STP-solver to operate on triangles instead of operating on edges and implicitly guarantee the decomposition of the constraint graph according to its articulation points. We also provide extensive empirical evaluations of all known algorithms for solving the STP on sets of randomly generated problems. Our experiments demonstrate significant improvements of ¢ STPsolver, in terms of number of constraint checks and CPU time, over previously reported algorithms such as the Floyd-Warshall algorithm (F-W) [5;
In this paper, we provide a practical framework for characterizing, evaluating and selecting refo... more In this paper, we provide a practical framework for characterizing, evaluating and selecting reformulation techniques for reasoning about physical systems, with the long-term goal of automating the selection and application of these techniques. We view reformulation as a mapping from one encoding of a problem to another. A problem solving task is in turn accomplished by the application of a sequence of reformulations to an initial problem encoding to produce a final encoding that addresses the task. Our framework provides the terminology to specify the conditions under which a particular reformulation technique is applicable, the cost associated with performing the reformulation, and the effects of the reformulation with respect to the problem encoding. As such it provides the vocabulary to characterize the selection of a sequence of reformulation techniques as a planning problem. Our framework is sufficiently flexible to accommodate previously proposed properties and metrics for reformulation. We have used the framework to characterize a variety of reformulation techniques, three of which are presented in this paper.
Proceedings of the 4th International Symposium on Abstraction, Reformulation, and Approximation
Abstraction, reformulation, and approximation : 4th International Symposium, SARA 2000, Horseshoe Bay, USA, July 26-29, 2000 : proceedings
Springer eBooks, 2000
... Uther, Manuela M. Veloso (Carnegie Mellon University) Reformulating Propositional Satisfiabil... more ... Uther, Manuela M. Veloso (Carnegie Mellon University) Reformulating Propositional Satisfiability as Constraint Satisfaction 233 Toby Walsh (University ... P. Fries (coastal Carolina University), James H. Graham (University of Louisville) A Compositional Approach to Causality 309 ...
A Comparative Study of Arc-Consistency Algorithms
Arc consistency plays an important role in Constraint Satisfaction Problems (CSPs). Several algor... more Arc consistency plays an important role in Constraint Satisfaction Problems (CSPs). Several algorithms have been made to deal with arc consistency. AC-3, AC-4, AC-7 are very famous algorithms in this area. Our work is tried to figure out, which one is better to use. We judge it not only by constrain checks but also by the CPU time and so on. Based on AC algorithms, we implement Maintaining Arc consistency (MAC), and compare the performance of MAC-3, MAC-4 with FC.
Proceedings of the AAAI Conference on Artificial Intelligence
Freuder and Elfe (1996) introduced Neighborhood Inverse Consistency (NIC) as a strong local consi... more Freuder and Elfe (1996) introduced Neighborhood Inverse Consistency (NIC) as a strong local consistency property for binary CSPs. While enforcing NIC can significantly filter the variables domains, the proposed algorithm is too costly to be used on dense graphs or for lookahead during search. In this paper, we introduce and characterize Relational Neighborhood Inverse Consistency (RNIC) as a local consistency property that operates on the dual graph of a non-binary CSP. We describe and characterize a practical algorithm for enforcing it. We argue that defining RNIC on the dual graph unveils unsuspected opportunities to reduce the computational cost of our algorithm and increase its filtering effectiveness. We show how to achieve those effects by modifying the topology of the dual graph, yielding new variations the RNIC property. We also introduce an adaptive strategy to automatically select the appropriate property to enforce given the connectivity of the dual graph. We integrate th...
Proceedings of the AAAI Conference on Artificial Intelligence
Consistency properties and algorithms for achieving them are at the heart of the success of Const... more Consistency properties and algorithms for achieving them are at the heart of the success of Constraint Programming. In this paper, we study the relational consistency property R(*,m)C, which is equivalent to m-wise consistency proposed in relational databases. We also define wR(*,m)C, a weaker variant of this property. We propose an algorithm for enforcing these properties on a Constraint Satisfaction Problem by tightening the existing relations and without introducing new ones. We empirically show that wR(*,m)C solves in a backtrack-free manner all the instances of some CSP benchmark classes, thus hinting at the tractability of those classes.
In this document, we describe two tree-based algorithms for computing all k-combinations and k-co... more In this document, we describe two tree-based algorithms for computing all k-combinations and k-compositions of a finite set. We have developed two algorithms for solving the following combinatorial tasks: • Given a finite set S and a natural number k, find all subsets of S of size k. In the literature, this problem is called k-subsets and k-combinations. • Given two natural numbers k, n where k [less than or equal to] n, find all k-compositions of n where a k-composition is an ordered combination of k nonzero natural numbers whose sum is n. Note that in the literature, a k-composition of n can have null numbers. Further, some authors require that the sum of the k numbers to be less or equal to n. Both algorithms are based on building an intermediary tree data-structure. Using similar tree structures for generating various combinatorial objects under constraints is a “reasonably standard approach” [Hartke 2010]. Algorithms exist in the literature for k-combinations and k-compositions...
Proceedings of the AAAI Conference on Artificial Intelligence
Computing the minimal network of a Constraint Satisfaction Problem (CSP) is a useful and difficul... more Computing the minimal network of a Constraint Satisfaction Problem (CSP) is a useful and difficult task. Two algorithms, PerTuple and AllSol, were proposed to this end. The performances of these algorithms vary with the problem instance. We use Machine Learning techniques to build a classifier that predicts which of the two algorithms is likely to be more effective.
Proceedings of the AAAI Conference on Artificial Intelligence
The tractability of a Constraint Satisfaction Problem (CSP)is guaranteed by a direct relationship... more The tractability of a Constraint Satisfaction Problem (CSP)is guaranteed by a direct relationship between its consistencylevel and a structural parameter of its constraint network suchas the treewidth. This result is not widely exploited in practicebecause enforcing higher-level consistencies can be costlyand can change the structure of the constraint network andincrease its width. Recently, R(*,m)C was proposed as a relational consistency property that does not modify the structureof the graph and, thus, does not affect its width. In this paper,we explore two main strategies, based on a tree decomposition of the CSP, for improving the performance of enforcingR(*,m)C and getting closer to the above tractability condition. Those strategies are: a) localizing the application ofthe consistency algorithm to the clusters of the tree decomposition, and b) bolstering constraint propagation betweenclusters by adding redundant constraints at their separators,for which we propose three new sc...
Proceedings of the AAAI Conference on Artificial Intelligence
In Constraint Processing, many algorithms for enforcing the same level of local consistency may e... more In Constraint Processing, many algorithms for enforcing the same level of local consistency may exist. The performance of those algorithms varies widely. In order to understand what problem features lead to better performance of one algorithm over another, we utilize an algorithm configurator to tune the parameters of a random problem generator and maximize the performance difference of two consistency algorithms for enforcing constraint minimality. Our approach allowed us to generate instances that run 1000 times faster for one algorithm over the other.
Proceedings of the AAAI Conference on Artificial Intelligence
We propose to exploit cycles in the constraint network of a Constraint Satisfaction Problem (CSP)... more We propose to exploit cycles in the constraint network of a Constraint Satisfaction Problem (CSP) to vehicle constraint propagation and improve the effectiveness of local consistency algorithms. We focus our attention on the consistency property Partition-One Arc-Consistency (POAC), which is a stronger variant of Singleton Arc-Consistency (SAC). We modify the algorithm for enforcing POAC to operate on a minimum cycle basis (MCB) of the incidence graph of the CSP. We empirically show that our approach improves the performance of problem solving and constitutes a novel and effective localization of consistency algorithms. Although this paper focuses on POAC, we believe that exploiting cycles, such as MCBs, is applicable to other consistency algorithms and that our study opens a new direction in the design of consistency algorithms. This research is documented in a technical report (Woordward, Choueiry, and Bessiere 2016). http://consystlab.unl.edu/our_work/StudentReports/TR-UNL-CSE-20...
Contributions 1.The property Relational Neighborhood Inverse Consistency (RNIC) 2.Characterizatio... more Contributions 1.The property Relational Neighborhood Inverse Consistency (RNIC) 2.Characterization of RNIC in relation to previously known properties3.An efficient algorithm for enforcing RNIC, bounded by degree of the dual graph 4.Three reformulations of the dual graph to address topological limitations of the dual graph 5.An adaptive, automatic selection policy for choosing the appropriate dual graph 6.Empirical evidence on difficult CSP benchmarks Definition A Constraint Satisfaction Problem (CSP) is a combinatorial decision problem defined by a set of variables {A,B,C,…}, a set of domain values for these variables, and a set of constraints {R1,R2,R3,…} restricting the allowable combinations of values for variables. The task is to find a solution (i.e., an assignment of a value to each variable satisfying all constraints), or to find all such solutions. Local Consistency Local consistency is at the heart of Constraint Processing. It guarantees that all values (or tuples) particip...
Lecture Notes in Computer Science, 2018
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Papers by Berthe Y Choueiry