Practical combinatorial algorithms

组合对象，如字符串、排列、树和图，经常被用作模拟现实世界问题的基本构建块。例如，DNA序列可以被认为是由C、G、a、T四个字符组成的字符串。无线网络中的移动电话路由可以用简单无向图中的路径来建模。将算法应用于组合对象的其他应用包括：音乐作曲、敲钟、戏剧表演和量子纠错码。是的，组合算法用于艺术和科学的所有领域！通过用基本组合对象对这些现实世界的问题建模，我们获得了丰富的数学知识，可以应用于解决问题。该研究计划的主要目标是扩展这些核心组合对象的算法的简单性和效率，并使其他研究人员更容易访问它们。这些问题的本质有助于实现另一个目标，即吸引本科水平的学生，让他们对与基础数学对象相关的计算问题感到兴奋。指导和培训下一代是这个研究项目的核心。

Combinatorial objects such as strings, permutations, trees and graphs are often used as the fundamental building blocks to model real world problems. For instance, DNA sequences can be though of as strings over a four character alphabet C,G,A,T. Routing your mobile calls in wireless networks can be modelled by paths in simple undirected graphs. Other applications that apply algorithms on combinatorial objects include: musical composition, bell-ringing, theatrics, and quantum error correcting codes. Yes, combinatorial algorithms are used in all areas of the arts and sciences! By modelling these real world problems with fundamental combinatorial objects we gain access to a wealth of mathematical knowledge that can be applied to solve the problem. A primary objective of this research program is to expand the simplicity and efficiency of algorithms for these core combinatorial objects AND to make them more accessible to other researchers. The very nature of these problems helps to achieve another objective which is to engage students at the undergraduate level and get them excited about computational problems related to fundamental mathematical objects. Mentoring and training the next generation is at the core of this research program.