Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, March 10, 2005, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Jan Remy

Approximation Schemes for Node-Weighted Geometric Steiner Tree Problems

In this paper, we consider the following variant of the geometric Steiner tree problem. Every point u which is not included in the tree costs a penalty of π(u) units. Furthermore, every Steiner point we use costs c_S units. The goal is to minimize the total length of the tree plus the penalties. We prove that the problem admits a polynomial time approximation scheme. Our PTAS uses a new technique which allows us to avoid the so-called Patching Lemma [Arora 98] or equivalents. It may thus open new possibilities to find approximation schemes for geometric optimization problems that include complicated topology. Furthermore the techniques we use provide a more general framework which can be applied to geometric optimization problems with more complex objective functions.

(Joint work with Angelika Steger)

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