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New Results on MWT Subgraphs Oswin Aichholzer

Summary: New Results on MWT Subgraphs
Oswin Aichholzer
Franz Aurenhammer
Reinhard Hainz
Institute for Theoretical Computer Science
Graz University of Technology
Klosterwiesgasse 32/2, A-8010 Graz, Austria
e-mail: foaich,aureng@igi.tu-graz.ac.at
Let P be a polygon in the plane. We disprove the conjecture that the so-called LMT-
skeleton coincides with the intersection of all locally minimal triangulations, LMT (P ),
even for convex polygons P . We introduce an improved LMT-skeleton algorithm which,
for any simple polygon P , exactly computes LMT (P ), and thus a larger subgraph of the
minimum-weight triangulation MWT (P ). The algorithm achieves the same in the general
point set case provided the connectedness of the improved LMT-skeleton, which is given
in allmost all practical instances.
We further observe that the -skeleton of P is a subset of MWT (P ) for all values


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


Collections: Computer Technologies and Information Sciences