The complexity of the constraint satisfaction problem and its variants

约束满足问题及其变体的复杂性

• 批准号: RGPIN-2015-04656
• 负责人: Bulatov, Andrei
• 金额: $ 3.13万
• 依托单位: Simon Fraser University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=646508
• 关键词: complexity; constraint; satisfaction; problem; its

The constraint satisfaction problem (CSP) provides a general framework in which it is possible to express, in a natural way, a wide variety of problems. The aim in a CSP is to find an assignment of values to a given set of variables, subject to constraints on the values which can be simultaneously assigned to certain specified subsets of variables; in the counting constraint satisfaction problem the objective is to find the number of such assignments. The CSP is therefore very important in a number of applications, both theoretical and practical. In theoretical applications we look for new algorithmic ideas that can help to solve problems that could not be solved before, to improve the existing algorithms, to design more general and uniform algorithms, and to find evidence that certain problems are not efficiently solvable in the general case. In practical applications, constraint and satisfiability solvers are now standard tools in a wide range of areas from scheduling to hardware verification. Advances in the study of the CSP will speed up such solvers and expand their area of applicability.*** This project will contribute in both aspects of constraint problems, although its main focus is on the theoretical side. One of its main goals is to precisely understand which CSPs can be solved efficiently and design an efficient solution algorithm. This is one of the long standing open problems in computer science, but there is evidence that we may be approaching its resolution. Another component of the project is the study of counting constraint satisfaction problems. This area has unlikely connections to statistical physics, where such numbers affect the properties of large ensembles of particle, and, in particular,  help to locate phase transition thresholds, at which, for instance, liquid turns to gas. Finally, this project proposes to study the efficiency and to design new algorithms in the framework that is closer to practical circumstances than the standard worst case approach. It is known that practical problems tend to have a certain property called the power law distribution, and we plan to mathematically study the behaviour of various algorithms on instance of the CSP satisfying this property.**

约束满足问题(CSP)提供了一个通用的框架，在该框架中可以以自然的方式表达各种各样的问题。CSP的目标是找出给定变量集的赋值，约束条件是可以同时赋值给特定变量子集的值；在计数约束满足问题中，目标是找出这种赋值的数目。因此，CSP在许多应用中都非常重要，无论是在理论上还是在实践中。在理论应用中，我们寻找新的算法思想，帮助解决以前无法解决的问题，改进现有的算法，设计更通用和统一的算法，并找到某些问题在一般情况下不能有效求解的证据。在实际应用中，约束和可满足性求解器现在是从调度到硬件验证等广泛领域的标准工具。CSP研究的进展将加快这种求解器的速度并扩大其适用范围。*尽管该项目的主要重点是理论方面，但它将在约束问题的两个方面做出贡献。它的主要目标之一是准确地了解哪些CSP问题可以有效地求解，并设计一个高效的求解算法。这是计算机科学中长期悬而未决的问题之一，但有证据表明，我们可能正在接近它的解决方案。该项目的另一个组成部分是计数约束满足问题的研究。这个领域不太可能与统计物理有关，在统计物理学中，这样的数字会影响大型粒子系综的性质，特别是有助于定位相变阈值，例如，在相变阈值下，液体变成气体。最后，本项目建议研究效率，并在比标准最坏情况方法更接近实际情况的框架下设计新的算法。众所周知，实际问题往往具有一种称为幂分布的性质，我们计划在满足该性质的CSP实例上从数学上研究各种算法的行为。