Practical combinatorial 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. 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.