Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

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 cS 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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