Web pages of Lars Relund Nielsen

My Ph.D. spring 2000

I have started a project on bicriterion shortest hyperpaths (bi-SBT) together with my supervisor Kim Allan Andersen. This is a totally new research area, and we have to start from scratch by defining a bicriterion hypergraph and formulating the bi-SBT problem.

First, I began studying the bicriterion shortest path problem and the methods to solve it. There are two main approaches, namely node labeling and path/tree. The node labeling approach seems to be hard to transfer to hypergraphs because a hyperpath has a more complex structure than a path, resulting in more complex node labeling procedure. Furthermore, an efficient path satisfies that its subpaths are efficient; this is not always the case for hyperpaths. The path/tree approach seems more adaptable to hypergraphs. Most papers use a k’th shortest path subprocedure to solve the problem. Therefore I first developed methods to solve the k’th shortest hyperpath problem.

Conferences: “Probabilistic methods in combinatorial optimization”, BRICS, University of Aarhus, August 28 – 31, 2000.

Courses: “Logical inference II” – Study group in logic inference concerning how the use of mathematical programming methods can be used in logic inference.

Teaching: Student assistant in “Statistic for biologists” (Biostat – 1 class).

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