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: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=688721
• 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.**

约束满意度问题（CSP）提供了一个一般框架，在这种框架中，可以自然地表达各种各样的问题。 CSP的目的是找到对给定变量集的值的分配，这要受到可以简单地将其分配给某些指定变量指定子集的值的约束；在计数约束满意度问题中，目标是找到此类作业的数量。因此，在实际应用中，CSP非常重要，限制和满意度求解器现在是从计划到硬件验证的广泛领域的标准工具。对CSP的研究进展将加快此类求解器并扩大其适用性。***该项目将在约束问题的两个方面做出贡献，尽管其主要重点是理论方面。它的主要目标之一是精确了解哪些CSP可以有效地解决并设计有效的解决方案算法。这是计算机科学中长期存在的开放问题之一，但是有证据表明我们可能正在解决其解决方案。该项目的另一个组成部分是计算约束满意度问题的研究。该区域与统计物理学有不可能的连接，在这种情况下，这种数字会影响粒子大体组合的特性，尤其是有助于定位相变阈值，例如，液体转向气体。最后，该项目的建议是研究效率并设计新算法的框架中，该算法比标准最坏情况的方法更接近实际情况。众所周知，实际问题倾向于具有某种称为权力法分配的特性，我们计划以满足此属性的CSP来数学研究各种算法的行为。**