Using Restarts in Constraint Programming over Finite Domains - An Experimental Evaluation

The use of restart techniques in complete Satisfiability (SAT) algorithms has made solving hard real world instances possible. Without restarts such algorithms could not solve those instances, in practice. State of the art algorithms for SAT use restart techniques, conflict clause recording (nogoods), heuristics based on activity variable in conflict clauses, among others. Algorithms for SAT and Constraint problems share many techniques; however, the use of restart techniques in constraint programming with finite domains (CP(FD)) is not widely used as it is in SAT. We believe that the use of restarts in CP(FD) algorithms could also be the key to efficiently solve hard combinatorial problems. In this PhD thesis we study restarts and associated techniques in CP(FD) solvers. In particular, we propose to including in a CP(FD) solver restarts, nogoods and heuristics based in nogoods as this should improve search algorithms, and, consequently, efficiently solve hard combinatorial problems. We thus intend to: a) implement restart techniques (successfully used in SAT) to solve constraint problems with finite domains; b) implement nogoods (learning) and heuristics based on nogoods, already in use in SAT and associated with restarts; and c) evaluate the use of restarts and the interplay with the other implemented techniques. We have conducted the study in the context of domain splitting backtrack search algorithms with restarts. We have defined domain splitting nogoods that are extracted from the last branch of the search algorithm before the restart. And, inspired by SAT solvers, we were able to use information within those nogoods to successfully help the variable selection heuristics. A frequent restart strategy is also necessary, since our approach learns from restarts

A Theoretical Comparison of Resolution Proof Systems for CSP Algorithms

Many problems from a variety of applications such as graph coloring and circuit design can be modelled as constraint satisfaction problems (CSPs). This provides strong motivation to develop effective algorithms for CSPs. In this thesis, we study two resolution-based proof systems, NG-RES and C-RES, for finite-domain CSPs which have a close connection to common CSP algorithms. We give an almost complete characterization of the relative power among the systems and their restricted tree-like variants. We demonstrate an exponential separation between NG-RES and C-RES, improving on the previous super-polynomial separation, and present other new separations and simulations. We also show that most of the separations are nearly optimal. One immediate consequence of our results is that simple backtracking with 2-way branching is exponentially more powerful than simple backtracking with d-way branching

An Overview of Backtrack Search Satisfiability Algorithms

Propositional Satisfiability (SAT) is often used as the underlying model for a significan

Consistency and Random Constraint Satisfaction Models

In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to improve the efficiency of CSP algorithms, is in fact the key to the design of random CSP models that have interesting phase transition behavior and guaranteed exponential resolution complexity without putting much restriction on the parameter of constraint tightness or the domain size of the problem. We propose a very flexible framework for constructing problem instances withinteresting behavior and develop a variety of concrete methods to construct specific random CSP models that enforce different levels of constraint consistency. A series of experimental studies with interesting observations are carried out to illustrate the effectiveness of introducing structural elements in random instances, to verify the robustness of our proposal, and to investigate features of some specific models based on our framework that are highly related to the behavior of backtracking search algorithms

Breaking Instance-Independent Symmetries In Exact Graph Coloring

Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI, such as planning, time-tabling and scheduling. Provably optimal solutions may be desirable for commercial and defense applications. Additionally, for applications such as register allocation and code optimization, naturally-occurring instances of graph coloring are often small and can be solved optimally. A recent wave of improvements in algorithms for Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests generic problem-reduction methods, rather than problem-specific heuristics, because (1) heuristics may be upset by new constraints, (2) heuristics tend to ignore structure, and (3) many relevant problems are provably inapproximable. Problem reductions often lead to highly symmetric SAT instances, and symmetries are known to slow down SAT solvers. In this work, we compare several avenues for symmetry breaking, in particular when certain kinds of symmetry are present in all generated instances. Our focus on reducing CSPs to SAT allows us to leverage recent dramatic improvement in SAT solvers and automatically benefit from future progress. We can use a variety of black-box SAT solvers without modifying their source code because our symmetry-breaking techniques are static, i.e., we detect symmetries and add symmetry breaking predicates (SBPs) during pre-processing. An important result of our work is that among the types of instance-independent SBPs we studied and their combinations, the simplest and least complete constructions are the most effective. Our experiments also clearly indicate that instance-independent symmetries should mostly be processed together with instance-specific symmetries rather than at the specification level, contrary to what has been suggested in the literature

Parallel Pattern Search in Large, Partial-Order Data Sets on Multi-core Systems

Monitoring and debugging distributed systems is inherently a difficult problem. Events collected during the execution of distributed systems can enable developers to diagnose and fix faults. Process-time diagrams are normally used to view the relationships between the events and understand the interaction between processes over time. A major difficulty with analyzing these sets of events is that they are usually very large. Therefore, being able to search through the event-data sets can enable users to get to points of interest quickly and find out if patterns in the dataset represent the expected behaviour of the system. A lot of research work has been done to improve the search algorithm for finding event-patterns in large partial-order datasets. In this thesis, we improve on this work by parallelizing the search algorithm. This is useful as many computers these days have more than one core or processor. Therefore, it makes sense to exploit this available computing power as part of an effort to improve the speed of the algorithm. The search problem itself can be modeled as a Constraint Satisfaction Problem (CSP). We develop a simple and efficient way of generating tasks (to be executed by the cores) that guarantees that no two cores will ever repeat the same work-effort during the search. Our approach is generic and can be applied to any CSP consisting of a large domain space. We also implement an efficient dynamic work-stealing strategy that ensures the cores are kept busy throughout the execution of the parallel algorithm. We evaluate the efficiency and scalability of our algorithm through experiments and show that we can achieve efficiencies of up to 80% on a 24-core machine

Florida Historical Quarterly, Vol. 44, Issues 1 & 2

THE EXPLORATION OF FLORIDA AND SOURCES ON THE FOUNDING OF ST. AUGUSTINE Luis Rafael AranaALTAR AND HEARTH: THE COMING OF CHRISTIANITY Michael V. GannonNOTE ABOUT THE BIRTHPLACE OF HERNANDO DE SOTO El Conde Canilleros and Ursula LambJEAN RIBAULT\u27S COLONIES IN FLORIDA M. Adele Francis Gorman THE MAN WHO WAS PEDRO MENENDEZ Albert ManucyDRAKE DESTROYS ST. AUGUSTINE: 1586 James W. CovingtonTHE ARCHITECTURE OF HISTORIC ST. AUGUSTINE: A PHOTOGRAPHIC ESSAY F. Blair ReevesFUNERALS AND FIESTAS IN EARLY EIGHTEENTH CENTURY ST.AUGUSTINE John J. TePaske THE EAST FLORIDA INDIANS UNDER SPANISH AND ENGLISH CONTROL: 1763-1765Robert L. Gold JANAS IN BRITISH EAST FLORIDA Kenneth H. Beeson, Jr. A FRENCH REPORT ON ST. AUGUSTINE IN THE 1770s Lee Kennett THE DELANEY MURDER CASE Helen Hornbeck TannerCONTRIBUTOR

Améliorer l'efficacité de l'algorithme CDCL : décompositions arborescentes de grandes instances, CDCL sans saut arrière et CDCL à ordre partiel

Cette thèse s'intéresse à l'amélioration des performances pratiques de l'algorithme CDCL (Conftict-Driven Clause Learning) pour la résolution du problème de satisfaisabilité des formules propositionnelles, ou problème SAT. Plus particulièrement, nous cherchons à diminuer la destruction de l'instanciation courante lors des étapes de saut arrière, qui peuvent occasionner la désinstanciation de nombreuses variables n'ayant aucun rapport direct avec le conflit à résoudre. Dans ce but, nous proposons trois approches différentes. La première est une amélioration de l'utilisabilité de la méthode déjà existante de décomposition implicite d'une instance SAT. Notre but principal est de permettre son application à des instances de plus grande taille possible, après avoir montré les limitations des implémentations existantes. Nous développons également deux variations de l'algorithme CDCL, le CDCL sans saut arrière et le CDCL à ordre partiel. Si le premier supprime totalement la notion de saut arrière en permettant la propagation des clauses unitaires à des niveaux de décision quelconques, le second rend le saut arrière plus sélectif, en désinstanciant uniquement les niveaux de décision qui dépendent du niveau de retour du saut arrière. Notre analyse est à la fois théorique, notamment par une analyse détaillée des propriétés de différentes variations des CDCL sans saut arrière et à ordre partiel, et pratique, puisque l'efficacité de nos contributions est évaluée en les implémentant comme modifications de solveurs SAT de l'état de l'art et en se servant de ces implémentations sur des instances SAT difficiles utilisées lors de compétitions internationales de solveurs.\ud ______________________________________________________________________________ \ud MOTS-CLÉS DE L’AUTEUR : problème SAT, satisfaisabilité, formules propositionnelles, CDCL, décomposition arborescente, retour arrière, ordre partiel