A quasi-polynomial time approximation scheme for minimum weight triangulation

Authors:
Jan Remy;Angelika Steger
Affiliations:
Institut für Theoretische Informatik, Zürich;Institut für Theoretische Informatik, Zürich
Venue:
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Year:
2006

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Abstract

The MINIMUM WEIGHT TRIANGULATION problem is to find a triangulation T* of minimum length for a given set of points P in the Euclidean plane. It was one of the few longstanding open problems from the famous list of twelve problems with unknown complexity status, published by Garey and Johnson [8] in 1979. Very recently the problem was shown to be NP-hard by Mulzer and Rote. In this paper, we present a quasi-polynomial time approximation scheme for MINIMUM WEIGHT TRIANGULATION.