Combinatorial and Graph Algorithms

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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.