Hachemi Bennaceur

Consistency problems in ER-schemas for database systems

At a conceptual level data modelling consists in providing a structured form of relevant inforrnation and to accompany structures with constraints in order to capture more semantics. Cardinality constraints are among the most popular classes of constraints in database models. While each constraint class is now well understood, little is done about their interaction since possible conflicts among them may appear. The global coherence of these constraints must be considered before creating the physical corresponding database. In order to help in database design, our aim is then to propose a tool for reasoning about a set of Cardinality constraints. We will treat the global coherence using mathematical programming technique. The analyses and the detection of invalid sub-schemas will be done using Fourier-Motzkin elimination.

A Comparison between SAT and CSP Techniques

The aim of this paper is to establish a connection between the propositional logic and the constraint based reasoning frameworks. This work is based on a translation of the satisfiability problem (SAT) into the binary constraint-satisfaction problem (CSP). The structure of the SAT problem and its associated CSP are then exploited together for characterizing tractable SAT problems, increasing the effectiveness of the classical reduction rules: unit clause and monotone literal rules, and expressing the arc and path consistency concepts with logical inference rules. This study leads to compare the behaviors of the DP and MAC procedures for solving respectively a SAT instance and its binary CSP expression.

An Incremental Branch-And-Bound Method for the Satisfiability Problem

The satisfiability problem is to check whether a set of clauses in propositional logic is satisfiable. If it is satisfiable, the incremental satisfiability problem is then to check whether satisfiability remains given additional clauses. This paper deals with an incremental branch-and-bound method which solves exactly both problems. This method includes flexible Lagrangean relaxations, metaheuristics, and judicious jumping back. This leads to an efficient implementation which compares favorably with the classical Davis-Putnam-Loveland procedure and its incremental version designed by Hooker. Numerous computational results are detailed.

Partition-k-AC: An Efficient Filtering Technique Combining Domain Partition and Arc Consistency

The constraint propagation process is a powerful tool for solving constraint satisfaction problems (CSPs). We propose a filtering technique which exploits at best this tool in order to improve the pruning efficiency. This technique, combining domain partition and arc consistency, generalizes and improves the pruning efficiency of the arc consistency, and the singleton arc consistency filtering techniques. The presented empirical results show the gain brought by this technique.

Combining arc-consistency and dual lagrangean relaxation for filtering CSPs

This paper presents a CSPs filtering method combining arc-consistency and dual Lagrangean relaxation techniques. First, we model the constraint satisfaction problem as a 0/1 linear integer program (IP); then, the consistency of a value is defined as an optimization problem on which a dual Lagrangean relaxation is defined. While solving the dual Lagrangean relaxation, values inconsistencies may be detected (dual Lagrangean inconsistent values); the constraint propagation of this inconsistency can be performed by arc-consistency. After having made the CSP arc-consistent, the process iteratively selects values of variables which may be dual Lagrangean inconsistent. Computational experiments performed over randomly generated problems show the advantages of the hybrid filtering technique combining arc-consistency and dual Lagrangean relaxation.

An exact algorithm for the constraint satisfaction problem: application to logical inference

Abstract The inference problem in propositional logic realizes a strong connection between Artificial Intelligence and Operational Research. It is now well-known that this problem can be formulated as a constraint satisfaction problem (CSP), whose system has a generalized covering type (we recall that a CSP consists in proving the emptiness of a domain defined by a set of diophantine constraints, or the existence of a solution). We propose a new method - denoted by FAST (Fast Algorithm for the constraint Satisfaction Test problems) - which allows an efficient solution of the CSP instances for logical inference. Computational results are reported for 3-SAT, 4-SAT and system expert type instances.

Characterizing SAT Problems with the Row Convexity Property

Using the literal encoding of the satisfiability problem (SAT) as a binary constraint satisfaction problem (CSP), we relate the path consistency concept and the row convexity of CSPs with the inference rules in the propositional logic field. Then, we use this result to propose a measure characterizing satisfiable and unsatisfiable 3-SAT instances. The correlation between the computational results allows us to validate this measure.

Valid inequality based lower bounds for WCSP

Most of efficient WCSP solving methods are based on arc consistency notion used to transform a WCSP into an equivalent one easier to solve. There are several forms of arc consistency : AC* [9], DAC* [8], FDAC* [8], EDAC* [4]. Recently, an Optimal Soft Arc Consistency (OSAC) was proposed [2]. But this technique requires much computing time since it is based on a large linear program. We propose in this work a new valid transformation based on modeling of the WCSP as a linear program easier to solve than the computing of OSAC. Preliminary experiments on random and structured problems are presented, showing the advantage of our technique.

Clique inference process for solving Max-CSP

In this paper we show that the clique concept can be ex- ploited in order to solve Max-CSP. We present a clique inference process which leads to construct linear systems useful for computing new lower bounds. The clique inference process is introduced in the PFC-MPRDAC (5) algorithm and the obtained algorithm is called PFC-MPRDAC+CBB (CBB for Clique Based Bound). The carried out experiments have shown that PFC-MPRDAC+CBB leads to obtain very encouraging results. clique is binary if it is a union of two subsets of two domains of the CSP. In this work, we propose a linear formulation for any binary clique and show how it can be used to propose a new linear models useful for solving Max-CSP. We then propose a clique inference process which leads to construct interesting linear systems useful for computing good lower bounds.

Boolean approch for representing and solving constraint-satisfaction problems

In this paper, we propose a new way for representing and solving constraintsatisfaction problems (CSPs). We first show that a CSP can be modelized by a single pseudo-Boolean function. Then some theoretical results establishing the links between a CSP and its associated pseudo-Boolean function are described. We propose a Branch and Bound method exploiting this representation for solving CSPs. This method follows the same scheme developed by the Forward-Checking procedure. The main difference between the Branch and bound method and the Forward-Checking method lies in the computation performed at every node of the search tree. The Branch and Bound method uses the constraints in an active way to infer a knowledge about the problem. Then a solution or failure may be detected quickly.