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Constraint Processing

Rina Dechter
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TLDR
Rina Dechter synthesizes three decades of researchers work on constraint processing in AI, databases and programming languages, operations research, management science, and applied mathematics to provide the first comprehensive examination of the theory that underlies constraint processing algorithms.
Abstract
Constraint satisfaction is a simple but powerful tool. Constraints identify the impossible and reduce the realm of possibilities to effectively focus on the possible, allowing for a natural declarative formulation of what must be satisfied, without expressing how. The field of constraint reasoning has matured over the last three decades with contributions from a diverse community of researchers in artificial intelligence, databases and programming languages, operations research, management science, and applied mathematics. Today, constraint problems are used to model cognitive tasks in vision, language comprehension, default reasoning, diagnosis, scheduling, temporal and spatial reasoning. In Constraint Processing, Rina Dechter, synthesizes these contributions, along with her own significant work, to provide the first comprehensive examination of the theory that underlies constraint processing algorithms. Throughout, she focuses on fundamental tools and principles, emphasizing the representation and analysis of algorithms. ·Examines the basic practical aspects of each topic and then tackles more advanced issues, including current research challenges ·Builds the reader's understanding with definitions, examples, theory, algorithms and complexity analysis ·Synthesizes three decades of researchers work on constraint processing in AI, databases and programming languages, operations research, management science, and applied mathematics Table of Contents Preface; Introduction; Constraint Networks; Consistency-Enforcing Algorithms: Constraint Propagation; Directional Consistency; General Search Strategies; General Search Strategies: Look-Back; Local Search Algorithms; Advanced Consistency Methods; Tree-Decomposition Methods; Hybrid of Search and Inference: Time-Space Trade-offs; Tractable Constraint Languages; Temporal Constraint Networks; Constraint Optimization; Probabilistic Networks; Constraint Logic Programming; Bibliography

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References
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TL;DR: A general algebraic formulation for a wide range of combinatorial problems including Satisfiability, Graph Colorability and Graph Isomorphism is described, and it is demonstrated that the complexity of solving this decision problem is determined in many cases by simple algebraic properties of the relational structures involved.
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Algorithms for Distributed Constraint Satisfaction: A Review

TL;DR: This paper describes a series of algorithms for solving distributed CSPs, i.e., the asynchronous backtracking, the asynchronous weak-commitment search, the distributed breakout, and distributed consistency algorithms.
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TL;DR: Given a set of r-variate integral polynomials, a cylindrical algebraic decomposition (cad) of euclidean r-space E r partitions E r into connected subsets compatible with the zeros of the poynomials.
Proceedings Article

Generalized arc consistency for global cardinality constraint

TL;DR: This paper presents an efficient way of implementing generalized arc consistency for a gcc based on a new theorem of flow theory and shows how this algorithm can efficiently be combined with other filtering techniques.