Applications of algebra to the study of fine-grained computational complexity of constraint satisfaction problems

代数在研究约束满足问题的细粒度计算复杂性中的应用

• 批准号: 238899-2011
• 负责人: Larose, Benoît
• 金额: $ 1.46万
• 依托单位: Concordia University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=570520
• 关键词: Applications; algebra; study; fine; grained

In a constraint satisfaction problem (CSP), one must assign values to variables that must satisfy various constraints; typical real world examples include scheduling problems, database queries, image-processing, and frequency assignment problems. In general, determining whether a CSP admits a solution is an algorithmic challenge, but it often happens in practice that the constraints are of a very restricted form, allowing the use of efficient methods to solve the CSP. Our long-term goal is to classify precisely what kinds of restrictions lead to these tractable CSP's. Our approach is based on an unexpected and fruitful connection between CSP's and universal algebra that was uncovered in the late 90's by P. Jeavons. In short, every family of constraints is transformed into a mathematical object whose algebraic properties somehow reflect the difficulty of solving the CSP. This algebraic approach has led to some major breakthroughs in the last 10 years in the study of the algorithmic complexity of constraint satisfaction problems.

在约束满意度问题（CSP）中，必须分配 对必须满足各种约束的变量的值；典型的 现实世界的示例包括调度问题，数据库查询， 图像处理和频率分配问题。一般来说， 确定CSP是否允许解决方案是算法 挑战，但实际上通常会发生约束 具有非常有限的形式，允许使用高效 解决CSP的方法。我们的长期目标是对 确切地导致这些限制导致这些限制 CSP的。我们的方法是基于意外而富有成果的 发现的CSP和通用代数之间的联系 在90年代末，P。Jeavons。简而言之 约束将其转换为数学对象 代数特性在某种程度上反映了解决的困难 CSP。 这种代数方法导致了一些重大突破 在过去的十年中，研究了算法复杂性 约束满意度问题。