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New Results on Minimum Weight Triangulations and the LMTSkeleton \Lambda

Summary: New Results on Minimum Weight Triangulations and the
LMT­Skeleton \Lambda
(Extended Abstract)
Reinhard Hainz, Oswin Aichholzer, Franz Aurenhammer
Institute for Theoretical Computer Science
Graz University of Technology
Klosterwiesgasse 32/2, A­8010 Graz, Austria
e­mail: frhainz---oaich---aureng@igi.tu­graz.ac.at
1 Introduction
A minimum weight triangulation (MWT) of a planar
point set S minimizes the sum of the edge lengths
among all triangulations of S. Computing a minimum
weight triangulation is an important and interesting
problem, whose complexity status is unknown. It is
one of the open problems listed at the end of Garey
and Johnson's book about NP­completeness [7].
In this work we present new methods to compute
a subgraph of every MWT, based on [6]. This leads
to an algorithm that computes the modified LMT­
Skeleton (see Section 3 for an definition) in near lin­


Source: Aurenhammer, Franz - Institute for Theoretical Computer Science, Technische Universität Graz
Technische Universität Graz, Institute for Software Technology


Collections: Computer Technologies and Information Sciences