Exploiting Structure in Satisfiability-Based Problem Solving

具有挑战性的组合问题，包括许多优化问题，几乎出现在科学、工程和商业以及应用计算机科学的所有领域。一种特殊的解决这些问题的软件方法，有时被称为基于可满足性或基于约束的问题求解，为面对这些问题的工作人员提供了一种模型和解决能力。不是组合问题求解专家的用户只需要用高级的、说明性的、规范的语言来描述他们的问题就可以获得解。基于这种方法的技术是非常新的，但在越来越多的问题上被证明是非常有效的。这项研究旨在解决当前技术的两个重要局限性。一个是未知如何使作为该技术核心的求解算法来开发可在下一个十年预期的非常高性能的硬件，包括非常大量的计算核心和可能的绝热量子退火处理器。第二是存在广泛的问题，最有效的算法被称为动态规划算法，但是模式和求解技术不利用这一点。尽管本质不同，这两个问题都可以通过利用问题实例的特殊结构属性的一般方法部分解决。然而，在实践中利用这些属性需要新的理论和算法，这是本项目的主题。

Challenging combinatorial problems, including many optimization problems, arise in almost all areas of science, engineering and business, and applied computer science.  A particular approach to software for solving these problems, sometimes called satisfiability-based or constraint-based problem solving, provides workers facing such problems with a model-and-solve capability.  Users who are not experts in combinatorial problem solving need only describe their problem in a high-level, declarative, specification language to obtain solutions.  Technology based on this approach is very new, but is being shown highly effective for a growing range of problems.  This research aims to address two important limitations of the current technology.  One is that it is unknown how to adapt the solving algorithms at the core of this technology to exploit very high performance hardware which can be expected in the next decade, involving either very large numbers of compute cores and possibly adiabatic quantum annealing processors.  The second is that there is a wide range of problems for which the most effective algorithms are known as dynamic programming algorithms, but mode-and-solve technologies do not exploit this.  While of a different nature, both of these problems may be addressed in part by general methods which exploit particular structural properties of problem instances.  Taking advantage of these properties in practice, though, required new theory and algorithms, which are the subject of this project.