Algebraic Methods in Search

本研究的主要主题是小组的应用- 各种各样的搜索问题的理论技术。 的 最终目标是将联合收割机代数技术与标准 搜索方法来解决目前可以解决的问题， 也不是单独的方法。 研究主要有三个方面： 开发用于测试算法思想的实验系统; 和探索的方法来表示搜索问题， 代数设置，以及解决这些问题的工具。 这些算法 研究发挥了核心作用，在大多数应用群论， 真实的世界问题。 组成员资格用于构造解决方案， 最小字算法对应于解的简化， 并且基的改变表示组数据的变换 构造成更适合于改进时间的域， 空间利用率 应用程序很多。 示例范围从 运筹学中运输问题到pin最小化 在VLSI中计数。 算法和应用程序都在实施中 在一个统一的环境中， 使用各种数据结构和方法进行实验。

The principal theme of this research is the application of group- theoretic techniques to a wide variety of search problems. The ultimate objective is to combine algebraic techniques with standard search methods to solve problems which are currently solvable by neither method alone. The research has three major aspects; the development of an experimental system for testing algorithmic ideas; and the exploration of methods for representing search problems in an algebraic setting, and of tools for solving them. The algorithms to be studied play a central role in most applications of group theory to real world problems. Group membership is used to construct a solution, minimum word algorithms correspond to the simplification of a solution, and a change of basis represents a transformation of the group data structure into a domain which is more suitable for improving time and space utilization. Applications are numerous. Examples range from the transporation problem in operations research to minimization of pin count in VLSI. Both algorithms and applications are being implemented in the context of a unified environment which is engineered to support experimentation with a variety of data structures and approaches.