Combinatorial and Graph Algorithms

组合对象，如字符串，排列，树和图通常被用作基本的积木模型真实的世界的问题。 例如，DNA序列可以被看作是四个字符字母表C、G、A、T上的字符串，并且在无线网络中路由您的移动的呼叫可以通过简单无向图中的路径来建模。 在这些组合对象上应用算法的其他应用包括：音乐作曲、敲钟、戏剧和量子纠错码。 是的，组合算法被用于艺术和科学的所有领域！ 将这些真实的世界问题抽象到组合层次的主要原因是获得关于特定组合对象的已知知识的丰富。 我的研究的主要目标之一是扩大这些核心组合对象的算法的质量和效率，并使它们更容易被其他研究人员使用。 在组合算法领域的学术研究的一个主要问题是获得开发的新算法。 在许多研究出版物中，算法或伪代码的概述通常在论文中提供。但是，在大多数情况下，没有提供代码实现。 因此，当另一个研究人员希望应用新算法时，他/她必须从头开始编写代码。 通常这些算法是足够复杂的，即使是有经验的程序员也很难复制代码。 虽然有一些Web应用程序确实提供了一个发布某些组合算法的场所，但它们要么过时，要么限制太多，要么不是免费的。 研究的目标之一是使应用程序现代化，使算法代码免费可用，并且研究人员可以轻松地贡献和访问。

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 and routing your mobile calls in wireless networks can be modeled by paths in simple undirected graphs. Other applications that apply algorithms on these 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! A primary reason to abstract these real world problems down to a combinatorial level is to gain access to a wealth of knowledge already known about a particular combinatorial object. One of the primary objectives of my research is to expand the quality and efficiency of algorithms for these core combinatorial objects AND to make them more accessible to other researchers. A major problem with academic research in the area of combinatorial algorithms is the access to the new algorithms developed. In many research publications, outlines of algorithms, or pseudocode, are often provided within the paper. However, in most cases no code implementation is provided. Thus, when another researcher wishes to apply the new algorithm, he/she has to start from square one writing up the code. Often these algorithms are of sufficient complexity that even experienced programmers have difficulty in reproducing the code. While there are some web applications that do provide a venue to distribute some combinatorial algorithms, they are either dated or are too restrictive or are not freely available. One of the goals of the research is to modernize an application to make algorithm code freely available, and easy for researchers to both contribute to and access.