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Computational Geometry { Some Easy Questions and their Recent Solutions

Summary: Computational Geometry { Some Easy
Questions and their Recent Solutions
Franz Aurenhammer
(Graz University of Technology, Graz, Austria
Abstract: We address three basic questions in computational geometry which can
be phrased in simple terms but have only recently received (more or less) satisfactory
answers: point set enumeration, optimum triangulation, and polygon decomposition.
Key Words: Computational geometry, combinatorial geometry, point set data base,
minimum-weight triangulation, polygonal skeleton
Categories: F.2.2
1 Introduction
Computational geometry is concerned with the algorithmic study of elemen-
tary geometric problems. Ever since its emergence as a new branch of computer
science in the early 1970's, a fruitful interplay has been taking place between
combinatorial geometry, algorithms theory, and more practically oriented ar-
eas of computer science. Computational geometry has been among the driving
forces for developing advanced algorithmic techniques, data structures, and set-
theoretic concepts. Parametric search, randomization, plane-sweep technique,
fractional cascading, and "-nets are a some examples. On the other hand, inter-


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


Collections: Computer Technologies and Information Sciences