Jon W. Van Laarhoven, Applied Mathematics and Computational Sciences, University of Iowa
I am a doctoral candidate in Applied Mathematics and Computational Sciences at the University of Iowa, and I anticipate graduation in May 2010.
I am advised by Professors Kurt Anstreicher and Jeffrey Ohlmann of the Management Sciences Department. In the left navigation bar, you will find supplementary materials
regarding my teaching, research, and talks.
Effective teaching is my number one focus. While at the University of Iowa, I have been priveliged to instruct mathematics as well as the martial art of Brazilian Jiu-jitsu. Teaching across these two disciplines has provided a diversity of experience which I believe has made me a more complete teacher.
My thesis research is on the Euclidean Steiner Tree Problem (ESTP), which asks for the shortest network (sum of edge lengths) spanning a set of terminal points with the freedom to add extra Steiner points to shorten the length of the network. Much work has been done on the ESTP in the plane, but less is known in higher dimensions. My research includes a heuristic for the ESTP in Rd for d=2...5. The algorithm utilizes the Delaunay triangulation to generate candidate Steiner points for insertion, but unlike other ESTP heuristics relying upon Delaunay triangulation, inserts Steiner points probabilistically into Delaunay triangles to achieve different subtrees on subsets of terminal nodes. The algorithm produces optimal or near-optimal solutions in reasonable computational times across various instance sizes and dimensions.
My research also includes work on an exact branch-and-bound algorithm for the ESTP. The main deficiency of the current state-of-the-art algorithm for d>2 is that the criterion for eliminating candidate partial Steiner topologies is quite weak, leading to rapid growth in the branch-and-bound tree. I present new geometric exclusion criteria which promote fathoming higher in the branch-and-bound tree and do so with much less computational effort than the usual length-based fathoming criteria. In addition to the ESTP, my other research interests include computational geometry, heuristic search, optimization, and mathematical modeling. A Liberal learner at heart, I look forward to future research opportunities involving collaboration across disciplines.
In my spare time, I am a blue belt and instructor of Brazilian Jiu-jitsu at the Hawkeye Brazilian Jiu-jitsu Club. Brazilian Jiu-jitsu originated in Brazil in the 1920's and was brought to the United States in the 1980's. Brazilian Jiu-jitsu is a grappling art which depends on locks and leverages to subdue a bigger, stronger opponent. A good Brazilian Jiu-jitsu match is much like a game of chess with attacks, counter-attacks, and finally, a "checkmate."
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