Constraint Logic Programming (CLP) is a merger of two declarative paradigms: constraint solving and logic programming. Although a relatively new field, CLP has progressed in several quite different directions. In particular, the early fundamental concepts have been adapted to better serve in different areas of applications. In this survey of CLP, a primary goal is to give a systematic description of the major trends in terms of common fundamental concepts. The three main parts cover the theory, implementation issues, and programming for applications.

this paper we argue that many user interface construction problems are handled more naturally and elegantly by multi-way constraints than by one-way constraints. We present pseudocode for an incremental multi-way constraint satisfaction algorithm, DeltaBlue, and describe experience in using the algorithm in two user interface toolkits. Finally, we provide performance figures demonstrating that multi-way constraint solvers can be entirely competitive in performance with one-way constraint solvers

Arising from research in the computer science community, constraint programming is a fairly new technique for solving optimization problems. For those familiar with mathematical programming, a number of language barriers make it difficult to understand the concepts of constraint programming. In this short tutorial on constraint programming, we explain how it relates to familiar mathematical programming concepts and how constraint programming and mathematical programming technologies are complementary. We assume a minimal background in linear and integer programming. G eorge Dantzig [1963] invented the simplex method for linear programming in 1947 and first described it in a paper entitled “Programming in a linear structure ” [Dantzig 1948, 1949]. Fifty years later, linear programming is now a strategictechnique used by thousands of businesses trying to optimize their global operations. In the mid-1980s, researchers developed constraint programming as a computer science technique by combining developments in the artificial intelligence community with the development of new computer programming languages. Fifteen years later, constraint programming is now being seen as an important technique that complements traditional mathematical programming technologies as businesses continue to look for ways to optimize their business operations. Developed independently as a technique within the computer science literature, constraint programming is now getting attention from the operations research com-

We address a global constraint for enforcing contiguity. Contiguity is the property that all of one kind of object in an array or list are grouped together; it is a one-dimensional discrete form of convexity. We present an implementation of this property in a concurrent constraint programming language. We adapt and apply the constraint propagation framework of [19] to analyse the contiguity property. In particular, the soundness of the implementation is proved and the forms of local consistency that are maintained by the implementation are identified. A complexity analysis shows that the implementation is optimal for achieving arc-consistency. However, an optimal implementation is not given for a stronger consistency condition, and we raise the possibility that an optimal implementation requires meta-level programming.

We develop a framework for addressing correctness and timeliness-of-propagation issues for reactive constraints - global constraints or user-defined constraints that are implemented through constraint propagation. The notion of propagation completeness is introduced to capture timeliness of constraint propagation. A generalized form of arc-consistency is formulated which unifies many local consistency conditions in the literature. We show that propagation complete implementations of reactive constraints achieve this arc-consistency when propagation quiesces. Finally, we use the framework to state and prove an impossibility result: that CHR cannot implement a common relation with a desirable degree of timely constraint propagation.

A generally applicable approach to N-dimensional spatial reasoning is described. The approach is founded on a unique representation based on ideas concerning "tesseral" addressing. This offers many computational advantages including minimal data storage, computationally efficient translation of data, and simple data comparison, regardless of the number of dimensions under consideration. The representation allows spatial attributes associated with objects to be expressed simply and concisely in terms of sets of addresses which can then be related using standard set operations expressed as constraints. The approach has been incorporated into a spatial reasoning system --- the SPARTA (SPAtial Reasoning using Tesseral Addressing) system --- which has been successfully used in conjunction with a significant number of spatial application domains. Keywords: Spatio-Temporal Reasoning, Tesseral Addressing, N-Dimensional information processing. 1 INTRODUCTION A versatile and generally applicabl...

Contents 1 Introduction 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Preliminaries on CLP over Finite Domain 4 2.1 Constraint Logic Programming . . . . . . . . . . . . . . . . . . . . . . . .4 2.2 Constraint Satisfaction Problem . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.1 Basics of Consistency . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.2 Variable and Value Ordering . . . . . . . . . . . . . . . . . . . . . 12 2.3 CLP Over Finite Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 Other Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.41 CLP(R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.41 Combining Consistency Techniques and Linear Programming . . . 17 3 Consistency on a Special Class of Constraints 19 3.1 Background . . . . . . . . . . . . . . . . .

Abstract. A deterministic cycle scheduling of partitions at the operating system level is supposed for a multiprocessor system. In this paper, we propose a tool for generating such schedules. We use constraint based programming and develop methods and concepts for a combined interactive and automatic partition scheduling system. This paper is also devoted to basic methods and techniques for modeling and solving this partition scheduling problem. Initial application of our partition scheduling tool has proved successful and demonstrated the suitability of the methods used. 1