Crossing Boundaries: Tapestry Within the Context of the 21st Century

International audienceGraphical model processing is a central problem in artificial intelligence. The optimization of the combined cost of a network of local cost functions federates a variety of famous problems including CSP, SAT and Max-SAT but also optimization in stochastic variants such as Markov Random Fields and Bayesian networks. Exact solving methods for these problems typically include branch and bound and local inference-based bounds.In this paper we are interested in understanding when and how dynamic programming based optimization can be used to efficiently enforce soft local consistencies on Global Cost Functions, defined as parameterized families of cost functions of unbounded arity. Enforcing local consistencies in cost function networks is performed by applying so-called Equivalence Preserving Transformations (EPTs) to the cost functions. These EPTs may transform global cost functions and make them intractable to optimize.We identify as tractable projection-safe those global cost functions whose optimization is and remains tractable after applying the EPTs used for enforcing arc consistency. We also provide new classes of cost functions that are tractable projection-safe thanks to dynamic programming.We show that dynamic programming can either be directly used inside filtering algorithms, defining polynomially DAG-filterable cost functions, or emulated by arc consistency filtering on a Berge-acyclic network of bounded-arity cost functions, defining Berge-acyclic network-decomposable cost functions. We give examples of such cost functions and we provide a systematic way to define decompositions from existing decomposable global constraints.These two approaches to enforcing consistency in global cost functions are then embedded in a solver for extensive experiments that confirm the feasibility and efficiency of our proposal

Set Constraint Model and Automated Encoding into SAT: Application to the Social Golfer Problem

On the one hand, Constraint Satisfaction Problems allow one to declaratively model problems. On the other hand, propositional satisfiability problem (SAT) solvers can handle huge SAT instances. We thus present a technique to declaratively model set constraint problems and to encode them automatically into SAT instances. We apply our technique to the Social Golfer Problem and we also use it to break symmetries of the problem. Our technique is simpler, more declarative, and less error-prone than direct and improved hand modeling. The SAT instances that we automatically generate contain less clauses than improved hand-written instances such as in [20], and with unit propagation they also contain less variables. Moreover, they are well-suited for SAT solvers and they are solved faster as shown when solving difficult instances of the Social Golfer Problem.Comment: Submitted to Annals of Operations researc

A Class of df-consistencies for Qualitative Constraint Networks

International audienceIn this paper, we introduce a new class of local consis- tencies, called °f-consistencies, for qualitative constraint networks. Each consistency of this class is based on weak composition (°) and a mapping f that provides a covering for each relation. We study the connections ex- isting between some properties of mappings f and the relative inference strength of °f-consistencies. The con- sistency obtained by the usual closure under weak com- position is shown to be the weakest element of the class, and new promising perspectives are shown to be opened by °f-consistencies stronger than weak composition. We also propose a generic algorithm that allows us to com- pute the closure of qualitative constraint networks un- der any "well-behaved" consistency of the class. The experimentation that we have conducted on qualitative constraint networks from the Interval Algebra shows the interest of these new local consistencies, in particular for the consistency problem

Supervisees' and supervisors' experiences of group climate in group supervision in psychotherapy. Effects of admission procedure

The purpose of this study was to evaluate the effects of two different admission procedures (high school grades/scholastic aptitude test (SAT) versus high school grades/SAT + interview) to a program in professional psychology on students' and supervisors' experiences of the group climate in psychotherapy supervision groups during an eighteen-month clinical practicum. A self-rating scale constructed to measure experiences of group climate in group supervision in psychotherapy was used. The results showed that students who were admitted based on the alternative admission procedure reported that their supervision groups had a more beneficial climate compared to those who were admitted based on high school grades/SAT. The evaluation suggested that admission via interviews together with high school grades/SAT is a good alternative to traditional admission procedures

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