Research

Research Summary

I have worked in a wide variety of areas throughout my career including areas that are highly theoretical as well as areas that are quite practical. My initial research work was in combinatorics and lattice theory. My thesis contains a number of interesting results about free distributive lattices and develops a theory of basis elements for arbitrary finite lattices that has proven useful in many situations. I periodically return to combinatorics and lattice theory because it provides a solid foundation for my other work.

In particular, my joint work with Larry Carter and Mark Wegman on the analysis of universal hashing functions made extensive use of the combinatorial skills that I had developed in my mathematical work. This analysis received a Research Division Award from IBM and resulted in a patent that I received along with Carter and Wegman.

My combinatorial skills were also crucial in the work that I did with Michael Wesley on constructing 3-dimensional objects from wireframes and projects. This work produced the first complete algorithms that could handle very complex datasets and could spot inconsistencies and impossibilities. We were able to provide previously unknown solutions for well-known mechanical drawing puzzles. This work was widely cited and resulted in Wesley and me being cited as among the Top 10 leading scientists in the field of Computer Vision (Visualizing a Knowledge Domain’s Intellectual Structure, Chen, Paul, IEEE Computer, March, 2001, pp. 65-71). This work received an Outstanding Innovation Award from IBM and was written up in the popular scientific press.

I have produced a variety of algorithms, including widely referenced algorithms for finding optimal Steiner Trees and multi-dimensional bin packing, as well as algorithms for coding theory, biology and networking. I have coauthored papers with a variety of outstanding researchers including Robert Tarjan (Turing Award Winner), Mark Wegman (IBM Fellow), and Frank Moss (Former Director of the MIT Media Lab).

I have written a number of papers in bioinformatics ranging from practical papers which found ways to improve phage typing sets to theoretical papers giving algorithms for factor-union systems and models for antibody-antigen systems.

I am also interested in practical problems. While at IBM, I built voice-controlled systems for people with quadriplegia and worked in other areas related to disabilities. Over the last several years, I have been moving into Cybersecurity and Cybersecurity education. As part of these efforts I ran workshops for NSF on Computing and Homeland Security, and also on Computing in Polar Environments. In 2010 and 2011 I ran a track on Cybersecurity Education at the International Conference on Security & Management. We will be running this track in 2012 as well.

My research interests are wide ranging, and I enjoy working on problems with people and also on my own.