Franz Aurenhammer Univ.-Prof. DI Dr. techn.

Institute for Theoretical Computer Science
Graz University of Technology

 

 


Publications

2016
Journal Article
Franz Aurenhammer and Gernot Christian Walzl Straight Skeletons and Mitered Offsets of Nonconvex Polytopes Show publication in PURE
Conference/Workshop Article
Franz Aurenhammer, Günter Paulini and Bert Jüttler Voronoi diagrams for parallel halflines in 3D Voronoi diagrams for parallel halflines in 3D Show publication in PURE
2015
Journal Article
Wolfgang Aigner, Franz Aurenhammer and Bert Jüttler On Triangulation Axes of Polygons Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, Wolfgang Aigner, Bert Jüttler, Katerina Dobiásová and G. Rote Triangulations with circular arcs Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, Thomas Hackl, Alexander Pilz, Birgit Vogtenhuber and Clemens Huemer 3-Colorability of Pseudo-Triangulations Show publication in PURE
2014
Journal Article
Oswin Aichholzer, Franz Aurenhammer, Thomas Hackl, Ferran Hurtado, Alexander Pilz, Pedro Ramos, Jorge Urrutia, Pavel Valtr and Birgit Vogtenhuber On k-Convex Point Sets Show publication in PURE
Franz Aurenhammer and Günter Paulini On shape Delaunay tessellations Show publication in PURE
Franz Aurenhammer, Bing Su, Yinfeng Xu and Binhai Zhu A note on visibility-constrained Voronoi diagrams Show publication in PURE
Conference/Workshop Article
Franz Aurenhammer and Gernot Christian Walzl Three-dimensional straight skeletons from bisector graphs Three-dimensional straight skeletons from bisector graphs 1-13 Show publication in PURE
Gernot Christian Walzl and Franz Aurenhammer Polytope Offsets and Straight Skeletons in 3D Polytope Offsets and Straight Skeletons in 3D 98-99 Show publication in PURE
2013
Conference/Workshop Article
Gernot Christian Walzl and Franz Aurenhammer Structure and Computation of Straight Skeletons in 3-Space Structure and Computation of Straight Skeletons in 3-Space 44-54 Show publication in PURE
2012
Journal Article
Franz Aurenhammer and Bert Jüttler On Computing the Convex Hull of (Piecewise) Curved Objects Show publication in PURE
Thomas Schiffer, Franz Aurenhammer and Markus Demuth Computing Convex Quadrangulations Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, E. Demaine, F. Hurtado, P.A. Ramos and Jorge Urrutia On k-convex polygons Show publication in PURE
Conference/Workshop Article
O. Aichholzer, W. Aigner, F. Aurenhammer, B. Jüttler, K. Dobiásová and G. Rote Triangulations with circular arcs Triangulations with circular arcs 296-307 Show publication in PURE
O. Aichholzer, W. Aigner, F. Aurenhammer and B. Jüttler Exact medial axis computation for triangulated solids with respect to piecewise linear metrics Exact medial axis computation for triangulated solids with respect to piecewise linear metrics 1-27 Show publication in PURE
Franz Aurenhammer On triangulation axes of polygons On triangulation axes of polygons 125-128 Show publication in PURE
2011
Journal Article
Oswin Aichholzer, Franz Aurenhammer, Thomas Hackl, Bert Jüttler, Margot Oberneder and Zbynek Sir Computational and structural advantages of circular boundary representation Show publication in PURE
2010
Journal Article
Oswin Aichholzer, Wolfgang Aigner, Franz Aurenhammer, Thomas Hackl, [No Value] Jüttler B., [No Value] Pilgerstorfer E. and [No Value] Rabl M. Divide-and conquer for Voronoi diagrams revisited Show publication in PURE
Conference/Workshop Article
Markus Demuth, Franz Aurenhammer and Axel Pinz Straight skeletons for binary shapes Straight skeletons for binary shapes 9-16 Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, Thomas Hackl, Clemens Huemer, Alexander Pilz and Birgit Vogtenhuber 3-Colorability of pseudo-triangulations 3-Colorability of pseudo-triangulations 21-24 Show publication in PURE
Oswin Aichholzer, Wolfgang Aigner, Franz Aurenhammer, Katerina Dobiásová and Bert Jüttler Arc Triangulations Arc Triangulations 17-20 Show publication in PURE
2009
Journal Article
Oswin Aichholzer, Wolfgang Aigner, Franz Aurenhammer, Thomas Hackl, Bert Jüttler and Margot Rabl Medial axis computation for planar free-form shapes Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, Thomas Hackl and Bettina Speckmann On minimum weight pseudo-triangulations Show publication in PURE
B. Aranaov , Franz Aurenhammer, F. Hurtado , S. Langerman , D. Rappaport , S. Smorodinsky and C. Seara Small weak epsilon nets Show publication in PURE
Conference/Workshop Article
Oswin Aichholzer, Wolfgang Aigner, Franz Aurenhammer, Thomas Hackl, Bert Jüttler, Elisabeth Pilgerstorfer and Margot Rabl Divide-and-conquer for voronoi diagrams revisited Divide-and-conquer for voronoi diagrams revisited 189-197 Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, Olivier Devillers, Thomas Hackl, Monique Teillaud and Birgit Vogtenhuber Lower and upper bounds on the number of empty cylinders and ellipsoids Lower and upper bounds on the number of empty cylinders and ellipsoids 139-142 Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, F. Hurtado, P.A. Ramos and Jorge Urrutia Two-convex polygons Two-convex polygons 117-120 Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, Bernhard Kornberger, Simon Plantinga, Günter Rote, Astrid Sturm and Gert Vegter Recovering structure from r-sampled objects Recovering structure from r-sampled objects 1349-1360 Show publication in PURE
Oswin Aichholzer, Wolfgang Aigner, Franz Aurenhammer, Thomas Hackl, Bert Jüttler, Elisabeth Pilgerstorfer and Margot Rabl Divide-and-conquer for voronoi diagrams revisited Divide-and-conquer for voronoi diagrams revisited 293-296 Show publication in PURE
2008
Book Chapter
Franz Aurenhammer and [No Value] Xu Y.-F. Optimal triangulationsOptimal triangulations2757-2764 Show publication in PURE
Journal Article
Oswin Aichholzer, Franz Aurenhammer, P. Gonzalez-Nava, Thomas Hackl, Clemens Huemer, F. Hurtado, Hannes Krasser, S. Ray and Birgit Vogtenhuber Matching edges and faces in polygonal partitions Show publication in PURE
Conference/Workshop Article
Franz Aurenhammer, Markus Demuth and Thomas Schiffer Computing convex quadrangulations Computing convex quadrangulations Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, Thomas Hackl, Bernhard Kornberger, Simon Plantinga, Günter Rote, Astrid Sturm and Gert Vegter Seed Polytopes for Incremental Approximation Seed Polytopes for Incremental Approximation 13-16 Show publication in PURE
2007
Journal Article
Oswin Aichholzer, Franz Aurenhammer, Thomas Hackl and Clemens Huemer Connecting colored point sets Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, Clemens Huemer and Birgit Vogtenhuber Gray Code Enumeration of Plane Straight Line Graphs Show publication in PURE
Franz Aurenhammer Weighted skeletons and fixed-share decomposition Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer and Thomas Hackl Pre-triangulations and liftable complexes Show publication in PURE
Conference/Workshop Article
Oswin Aichholzer, Franz Aurenhammer, Thomas Hackl and B. Speckmann On (pointed) minimum weight pseudo-triangulations On (pointed) minimum weight pseudo-triangulations 209-212 Show publication in PURE
Franz Aurenhammer, Johannes Wallner, Martin Peternell and Helmut Pottmann Voronoi diagrams for oriented spheres Voronoi diagrams for oriented spheres 33-37 Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, Thomas Hackl, Bert Jüttler, Margot Oberneder and Zbynek Sir Computational and structural advantages of circular boundary representation Computational and structural advantages of circular boundary representation 374-385 Show publication in PURE
Bernhard Kornberger, Thomas Hackl, Franz Aurenhammer, Oswin Aichholzer, Helmut Pottmann and Martin Peternell Approximating Boundary-Triangulated Objects with Balls Approximating Boundary-Triangulated Objects with Balls 130-133 Show publication in PURE
Other Article
Franz Aurenhammer, M. Peternell, Helmut Pottmann and J. Wallner Voronoi diagrams for oriented spheres Show publication in PURE
Franz Aurenhammer, B. Speckmann, Oswin Aichholzer and Thomas Hackl On (pointed) minimum weight pseudo-triangulations Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, B. Juettler, M. Oberneder, Z. Sir and Thomas Hackl Computational and structural advantages of circular boundary representation Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, Thomas Hackl, B. Kornberger , M. Peternell and Helmut Pottmann Approximating boundary-triangulated objects with balls Show publication in PURE
2006
Book
Franz Aurenhammer, [No Value] M. Peternell, [No Value] H. Pottmann and [No Value] J. Wallner Voronoi diagrams for oriented spheres Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, Thomas Hackl, B. Juettler, M. Oberneder and Z. Sir Computational and structural advantages of circular boundary representation Show publication in PURE
Franz Aurenhammer, B. Kornberger , M. Peternell , H. Pottmann, Oswin Aichholzer and Thomas Hackl Approximating boundary-triangulated objects with balls Show publication in PURE
Franz Aurenhammer, [No Value] R. L. S. Drysdale and [No Value] H. Krasser Farthest line segment Voronoi diagrams Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer and Thomas Hackl Connecting colored point sets Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, C. Huemer and Hannes Krasser Transforming spanning trees and pseudo-triangulations Show publication in PURE
Franz Aurenhammer and [No Value] H. Krasser Pseudo-simplicial complexes from maximal locally convex functions Show publication in PURE
Journal Article
Oswin Aichholzer, Franz Aurenhammer, C. Huemer and Hannes Krasser Transforming spanning trees and pseudo-triangulations Show publication in PURE
Franz Aurenhammer and [No Value] Krasser H Pseudo-simplicial complexes from maximal locally convex functions Show publication in PURE
Franz Aurenhammer, R. L. S. Drysdale and Hannes Krasser Farthest line segment Voronoi diagrams Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer and Hannes Krasser On the crossing number of complete graphs Show publication in PURE
Conference/Workshop Article
Oswin Aichholzer, Franz Aurenhammer, C. Huemer and Birgit Vogtenhuber Gray code enumeration of plane straight-line graphs Gray code enumeration of plane straight-line graphs 71-74 Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer and Thomas Hackl Pre-triangulations and liftable complexes Pre-triangulations and liftable complexes 282-291 Show publication in PURE
2005
Conference/Workshop Article
Oswin Aichholzer, Franz Aurenhammer, C. Huemer and Hannes Krasser Transforming spanning trees and pseudo-triangulations Transforming spanning trees and pseudo-triangulations 81-84 Show publication in PURE
Franz Aurenhammer Pre-triangulations: A generalization of Delaunay triangulations and flips Pre-triangulations: A generalization of Delaunay triangulations and flips 235-235 Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, P. Gonzalez-Nava, Thomas Hackl, C. Huemer, F. Hurtado, Hannes Krasser, S. Ray and Birgit Vogtenhuber Matching edges and faces in polygonal partitions Matching edges and faces in polygonal partitions 123-126 Show publication in PURE
Franz Aurenhammer and Hannes Krasser Pseudo-tetrahedral complexes Pseudo-tetrahedral complexes 85-88 Show publication in PURE
B. Aronov, Oswin Aichholzer, Franz Aurenhammer, F. Hurtado, S. Langerman, D. Rappaport, S. Smorodinsky and C. Seara Small weak epsilon nets Small weak epsilon nets 51-54 Show publication in PURE
2004
Journal Article
Oswin Aichholzer, Franz Aurenhammer and B. Palop Quickest paths, straight skeletons, and the city Voronoi diagram Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, H. Krasser and B. Speckmann Convexity minimizes pseudo-triangulations Show publication in PURE
2003
Journal Article
Oswin Aichholzer, Franz Aurenhammer, P. Brass and Hannes Krasser Pseudo-triangulations from surfaces and a novel type of edge flip Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, F. Hurtado and Hannes Krasser Towards compatible triangulations Show publication in PURE
Conference/Workshop Article
Franz Aurenhammer Pseudo-simplices and their derivation Pseudo-simplices and their derivation 11-11 Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, P. Brass and Hannes Krasser Spatial Embedding of Pseudo-Triangulations Spatial Embedding of Pseudo-Triangulations 144-153 Show publication in PURE
2002
Book
Oswin Aichholzer, Franz Aurenhammer and H. Krasser Progress on rectilinear crossing numbers Show publication in PURE
Journal Article
Oswin Aichholzer, Franz Aurenhammer and H. Krasser Points and combinatorics Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, Bernhard Brandstätter, Thomas Ebner, Hannes Krasser, Christian Magele and Martin Mühlmann Evolution strategy and hierarchical clustering Show publication in PURE
Oswin Aichholzer and Franz Aurenhammer Voronoi diagrams - computational geometry's favorite Show publication in PURE
Conference/Workshop Article
Oswin Aichholzer, Franz Aurenhammer and Belén Palop Quickest paths, straight skeletons, and the city Voronoi diagram Quickest paths, straight skeletons, and the city Voronoi diagram 151-159 Show publication in PURE
2001
Journal Article
Oswin Aichholzer, Franz Aurenhammer, Christian Icking, Rolf Klein, Elmar Langetepe and Günter Rote Generalized self-approaching curves Show publication in PURE
Conference/Workshop Article
Oswin Aichholzer, Franz Aurenhammer, B. Brandtstätter, H. Krasser, Christian Magele, Martin Mühlmann and Werner Renhart Evolution Strategy and Hierarchical Clustering Evolution Strategy and Hierarchical Clustering ?-? Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer and H. Krasser Enumerating order types for small point sets with applications Enumerating order types for small point sets with applications 11-18 Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, F. Hurtado and H. Krasser Towards Compatible Triangulations Towards Compatible Triangulations 101-110 Show publication in PURE
2000
Conference/Workshop Article
Oswin Aichholzer, Franz Aurenhammer and F. Hurtado Edge Operations on Non-Crossing Spanning Trees Edge Operations on Non-Crossing Spanning Trees 121-125 Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, B. Brandtstätter, Thomas Ebner, H. Krasser and Christian Magele Niching evolution strategy with cluster algorithms Niching evolution strategy with cluster algorithms ?-? Show publication in PURE
1999
Journal Article
Oswin Aichholzer, Franz Aurenhammer and Reinhard Hainz New results on MWT subgraphs Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, Danny Z. Chen, D.T. Lee and Evanthia Papadopoulou Skew Voronoi diagrams Show publication in PURE
1998
Journal Article
Oswin Aichholzer, Franz Aurenhammer, Günter Rote and Yinfeng Xu Constant-level greedy triangulations approximate the MWT well Show publication in PURE
Conference/Workshop Article
Oswin Aichholzer and Franz Aurenhammer Straight skeletons for general polygonal figures in the plane Straight skeletons for general polygonal figures in the plane 7-21 Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, Christian Icking, Rolf Klein, Elmar Langetepe and Günter Rote Generalized self-approaching curves Generalized self-approaching curves 15-18 Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, Christian Icking, Rolf Klein, Elmar Langetepe and Günter Rote Generalized self-approaching curves Generalized self-approaching curves 317-326 Show publication in PURE
1997
Conference/Workshop Article
Oswin Aichholzer, Reinhard Hainz and Franz Aurenhammer New results on minimum-weight triangulations and the LMT skeleton New results on minimum-weight triangulations and the LMT skeleton 4-6 Show publication in PURE
1996
Journal Article
Oswin Aichholzer, S.-W. Cheng, N. Katoh, Günter Rote, M. Taschwer, Yinfeng Xu and Franz Aurenhammer Triangulations intersect nicely Show publication in PURE
Conference/Workshop Article
Oswin Aichholzer and Franz Aurenhammer Straight skeletons for general polygonal figures Straight skeletons for general polygonal figures 117-126 Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, Günter Rote and Yinfeng Xu Constant-level greedy triangulations approximate the MWT well Constant-level greedy triangulations approximate the MWT well 309-318 Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer, Günter Rote and Yinfeng Xu New greedy triangulation algorithms New greedy triangulation algorithms 11-14 Show publication in PURE
Oswin Aichholzer and Franz Aurenhammer Straight skeletons for general polygonal figures in the plane Straight skeletons for general polygonal figures in the plane 117-126 Show publication in PURE
1995
Book
Oswin Aichholzer and Franz Aurenhammer Straight skeletons for general polygonal figures Show publication in PURE
Oswin Aichholzer, Franz Aurenhammer and Günter Rote Optimal graph orientation with storage applications Show publication in PURE
Journal Article
Oswin Aichholzer, D. Alberts, Franz Aurenhammer and B. Gärtner A novel type of skeleton for polygons Show publication in PURE
Conference/Workshop Article
Oswin Aichholzer, D. Alberts, Franz Aurenhammer and B. Gärtner Straight skeletons of simple polygons Straight skeletons of simple polygons 114-124 Show publication in PURE
1994
Journal Article
Franz Aurenhammer, [No Value] Forman M., [No Value] Idury R., [No Value] Schäffer A. and [No Value] Wagner F. Faster isometric embedding in products of complete graphs Show publication in PURE
Conference/Workshop Article
Oswin Aichholzer and Franz Aurenhammer Classifying hyperplanes in hypercubes Classifying hyperplanes in hypercubes 53-57 Show publication in PURE
Other Article
Oswin Aichholzer and Franz Aurenhammer Classifying hyperplanes in hypercubes Show publication in PURE
1993
Journal Article
Franz Aurenhammer Voronoi diagrams - a survey of a fundamental geometric data structure Show publication in PURE
Conference/Workshop Article
Franz Aurenhammer Geometric clustering and Voronoi-type partitions Geometric clustering and Voronoi-type partitions 93-94 Show publication in PURE

Publications before 1993

F. Aurenhammer and G. Stoeckl:
Searching for segments with largest relative overlap.

In Proc. 15th IFIP Conf. System Modelling and Optimization, Lecture Notes in Control and Information Sciences, volume 180, pages 77-84, Zuerich, Switzerland, 1992. Springer Verlag.

 

F. Aurenhammer and G. Stoeckl:
Searching for segments with largest relative overlap.

Information Processing Letters, 41:103-108, 1992. [Report B 91-10, FU Berlin, Germany, 1991].

 

F. Aurenhammer and O. Schwarzkopf:
A simple on-line randomized incremental algorithm for computing higher order Voronoi diagrams.

Int'l Journal of Computational Geometry & Applications, 2:363-381, 1992. Special Issue. [Report B 91-02, FU Berlin, Germany, 1991]. (Gzipped PostScript, 18 p., 92 KB).

 

F. Aurenhammer, F. Hoffmann, and B. Aronov.
Least-squares partitioning.

In Proc. 8th European Workshop on Computational Geometry CG '92, pages 55-57, Utrecht, the Netherlands, 1992.

 

F. Aurenhammer, F. Hoffmann, and B. Aronov.
Minkowski-type theorems and least-squares partitioning.

In Proc. 8th Ann. ACM Symp. Computational Geometry, pages 350-357, Berlin, Germany, 1992. [Report B-92-09, FU Berlin, Germany, 1992].

 

F. Aurenhammer, J. Hagauer, and W. Imrich.
Cartesian graph factorization at logarithmic cost per edge.

Computational Complexity, 2:331-349, 1992.

 

F. Aurenhammer and J. Hagauer.
Computing equivalence classes among the edges of a graph with applications.

Discrete Mathematics, 109:3-12, 1992. Special Issue. [IIG-Report-Series 271, TU Graz, Austria, 1989].

 

F. Aurenhammer, G. Stoeckl, and E. Welzl.
The post-office problem for fuzzy point sets.

In Proc. 7th Workshop on Computational Geometry CG '91, Lecture Notes in Computer Science, volume 553, pages 1-11, Bern, Switzerland, 1991. Springer Verlag. [Report B 91-07, FU Berlin, Germany, 1991].

 

F. Aurenhammer and G. Stoeckl.
On the peeper's Voronoi diagram.

SIGACT News, 22(4):50-59, 1991. [IIG-Report-Series 264, TU Graz, Austria, 1988]. (Gzipped PostScript, 10 p., 64 KB).

 

F. Aurenhammer and O. Schwarzkopf.
A simple on-line randomized incremental algorithm for computing higher order Voronoi diagrams.

In Proc. 7th Ann. ACM Symp. Computational Geometry, pages 142-151, North Conway, U.S.A., 1991.

 

F. Aurenhammer and J. Hagauer.
Recognizing binary Hamming graphs in O(n2 log n) time.

In Proc. 16th Int'l Workshop on Graph-Theoretical Concepts in Computer Science, Lecture Notes in Computer Science, volume 484, pages 90-98, Berlin, Germany, 1991. Springer Verlag.

 

F. Aurenhammer.
Using Gale transforms in computational geometry.

Mathematical Programming, B 52:179-190, 1991. Special Issue. [IIG-Report-Series 248, TU Graz, Austria, 1988].

 

F. Aurenhammer.
Voronoi diagrams -- a survey of a fundamental geometric data structure.

ACM Computing Surveys, 23(3):345-405, 1991. Habilitationsschrift. [Report B 90-09, FU Berlin, Germany, 1990].

 

F. Aurenhammer and G. Stoeckl.
Fenster - Voronoi Diagramme (Abstract).

In Tagungsband DMV Jubilaeumstagung, page 52, Bremen, Germany, 1990.

 

F. Aurenhammer, J. Hagauer, and W. Imrich.
Factoring Cartesian-product graphs at logarithmic cost per edge.

In Proc. MPS Conf. Integer Programming and Combinatorial Optimization IPCO'90, pages 29-44, Waterloo, Canada, 1990. [IIG-Report-Series 287, TU Graz, Austria, 1990].

 

F. Aurenhammer.
A new duality result concerning Voronoi diagrams.

Discrete & Computational Geometry, 5(3):243-254, 1990. [IIG-Report-Series 216, TU Graz, Austria, 1985].

 

F. Aurenhammer.
A relationship between Gale transforms and Voronoi diagrams.

Discrete Applied Mathematics, 28:83-91, 1990. [IIG-Report-Series 247, TU Graz, Austria, 1988].

 

F. Aurenhammer and J. Hagauer.
Computing equivalence classes among the edges of a graph with applications.

In Proc. Int'l Conf. Algebraic Graph Theory, page 11, Leibnitz, Austria, 1989.

 

F. Aurenhammer and H. Imai.
Geometric relations among Voronoi diagrams.

Geometriae Dedicata, 27:65-75, 1988. [IIG-Report-Series 228, TU Graz, Austria, 1986].

 

F. Aurenhammer.
Algorithmic aspects of Gale transforms (abstract).

In Proc. 13th 3-Ann. Int'l Symp. Mathematical Programming, page 176, Tokyo, Japan, 1988.

 

F. Aurenhammer.
Improved algorithms for discs and balls using power diagrams.

Journal of Algorithms, 9(2):151-161, 1988. [IIG-Report-Series 209, TU Graz, Austria, 1985].

 

F. Aurenhammer.
Linear combinations from power domains.

Geometriae Dedicata, 28:45-52, 1988. [IIG-Report-Series 243, TU Graz, Austria, 1987].

 

F. Aurenhammer.
On-line sorting of twisted sequences in linear time.

BIT, 28:194-204, 1988. [IIG-Report-Series 232, TU Graz, Austria, 1987].

 

F. Aurenhammer.
On-line sorting of twisted sequences in linear time.

In 2nd Workshop on Computational Geometry and Discrete Algorithms, Osaka, Japan, 1988.

 

F. Aurenhammer.
Using Gale transforms in computational geometry.

In Proc. 4th Workshop on Computational Geometry CG '88, Lecture Notes in Computer Science, volume 333, pages 202-216, Wuerzburg, Germany, 1988. Springer Verlag.

 

F. Aurenhammer and H. Imai.
Geometric relations among Voronoi diagrams.

In Proc. 4th Ann. STACS, Lecture Notes in Computer Science, volume 247, pages 53-65, Passau, Germany, 1987. Springer Verlag.

 

F. Aurenhammer.
A criterion for the affine equivalence of cell complexes in Rd and convex polyhedra in Rd+1.

Discrete & Computational Geometry, 2(1):49-64, 1987. [IIG-Report-Series 205, TU Graz, Austria, 1985].

 

F. Aurenhammer.
Jordan sorting via convex hulls of certain non-simple polygons.

In Proc. 3rd Ann. ACM Symp. Computational Geometry, pages 21-29, Waterloo, Canada, 1987.

 

F. Aurenhammer.
Power diagrams: properties, algorithms, and applications.

SIAM Journal on Computing, 16(1):78-96, 1987. [IIG-Report-Series F120, TU Graz, Austria, 1983].

 

F. Aurenhammer.
Recognizing polytopical cell complexes and constructing projection polyhedra.

Journal of Symbolic Computation, 3(3):249-255, 1987. [IIG-Report-Series 203, TU Graz, Austria, 1985].

 

F. Aurenhammer.
A new duality result concerning Voronoi diagrams.

In Proc. 13th Ann. ICALP, Lecture Notes in Computer Science, volume 226, pages 21-32, Rennes, France, 1986. Springer Verlag.

 

F. Aurenhammer.
The one-dimensional weighted Voronoi diagram.

Information Processing Letters, 22(3):119-123, 1986. [IIG-Report-Series F110, TU Graz, Austria, 1983].

 

F. Aurenhammer.
Gewichtete Voronoidiagramme.

In Workshop on Computational Geometry CG '85, Karlsruhe, Germany, 1985.

 

F. Aurenhammer and H. Edelsbrunner.
An optimal algorithm for constructing the weighted Voronoi diagram in the plane.

Pattern Recognition, 17(2):251-257, 1984. [IIG-Report-Series F109, TU Graz, Austria, 1983].

 

F. Aurenhammer.
Gewichtete Voronoi Diagramme: Geometrische Deutung und Konstruktions-Algorithmen.

PhD thesis, IIG-TU Graz, Austria, 1984. Report B53.

 

F. Aurenhammer.
On the generality of power diagrams.

IIG Report F126, TU Graz, Austria, 1983.

[1]

F. Aurenhammer and G. Walzl. Straight skeletons and mitered offsets of nonconvex polytopes. Discrete & Computational Geometry, 56:743-801, 2016. (PDF, 624 KB).

[2]

F. Aurenhammer, G. Paulini, and B. Jüttler. Voronoi diagrams for parallel halflines in 3D. In Proc. 32nd European Workshop on Computational Geometry EuroCG '2016, pages 127-130, Lugano, Switzerland, 2016. (PDF, 126 KB).

[3]

F. Aurenhammer and G. Walzl. Three-dimensional straight skeletons from bisector graphs. In Proc. 5th International Conference on Analytic Number Theory and Spatial Tessellations, Voronoi's Impact on Modern Science, volume 5, pages 15-29, Kiev, Ukraine, 2015. (PDF, 148 KB).

[4]

W. Aigner, F. Aurenhammer, and B. Jüttler. On triangulation axes of polygons. Information Processing Letters, 115:45-51, 2015. (PDF, 213 KB).

[5]

O. Aichholzer, F. Aurenhammer, T. Hackl, C. Huemer, A. Pilz, and B. Vogtenhuber. 3-colorability of pseudo-triangulations. Int'l Journal of Computational Geometry & Applications, 25:283-298, 2015. (PDF, 524 KB).

[6]

O. Aichholzer, W. Aigner, F. Aurenhammer, K. Cech Dobiasova, B. Jüttler, and G. Rote. Triangulations with circular arcs. Journal of Graph Algorithms and Applications, 19:43-65, 2015. (PDF, 437 KB).

[7]

F. Aurenhammer and G. Walzl. Polytope offsets and straight skeletons in 3D. In Proc. 30th Ann. ACM Symp. Computational Geometry, pages 98-99, Kyoto, Japan, 2014. (PDF, 516 KB).

[8]

F. Aurenhammer, B. Su, Y.-F. Xu, and B. Zhu. A note on visibility-constrained Voronoi diagrams. Discrete Applied Mathematics, 174:52-56, 2014. (PDF, 382 KB).

[9]

F. Aurenhammer and G. Paulini. On shape Delaunay tessellations. Information Processing Letters, 114(535-541), 2014. (PDF, 427 KB).

[10]

O. Aichholzer, F. Aurenhammer, T. Hackl, F. Hurtado, A. Pilz, P. Ramos, J. Urrutia, P. Valtr, and B. Vogtenhuber. On k-convex point sets. Computational Geometry: Theory and Applications, 47:809-832, 2014. (PDF, 542 KB).

[11]

M. Kapl, F. Aurenhammer, and B. Jüttler. Voronoi diagrams from distance graphs. In Proc. 29th European Workshop on Computational Geometry EuroCG 2013, pages 185-188, Braunschweig, Germany, 2013. (PDF, 381 KB).

[12]

M. Kapl, F. Aurenhammer, and B. Jüttler. Voronoi diagrams from (possibly disconnected) embeddings. In Proc. International Symposium on Voronoi Diagrams ISVD 2013, IEEE Computer Society, pages 47-50, St. Petersburg, Russia, 2013. (PDF, 723 KB).

[13]

M. Kapl, F. Aurenhammer, and B. Jüttler. Using scaled embedded distances to generate metrics for R2. In Proc. 14th IMA Conference on Mathematics of Surfaces, Birmingham, England, 2013. (PDF, 988 KB).

[14]

F. Aurenhammer and G. Walzl. Structure and computation of straight skeletons in 3-space. In Proc. 24th International Symposium on Algorithms and Computation ISAAC'13, Springer LNCS, volume 8283, pages 44-54, Hong Kong, 2013. (PDF, 409 KB).

[15]

F. Aurenhammer, R. Klein, and D.T. Lee. Voronoi Diagrams and Delaunay Triangulations. World Scientific Publishing Company, Singapore, 2013.

[16]

T. Schiffer, F. Aurenhammer, and M. Demuth. Computing convex quadrangulations. Discrete Applied Mathematics, 160:648-656, 2012. (PDF, 790 KB).

[17]

F. Aurenhammer and B. Jüttler. On computing the convex hull of (piecewise) curved objects. Mathematics in Computer Science, 6(3):261-266, 2012. (PDF, 150 KB).

[18]

W. Aigner, F. Aurenhammer, and B. Jüttler. On triangulation axes of polygons. In Proc. 28th European Workshop on Computational Geometry EuroCG '2012, pages 125-128, Assisi, Italy, 2012. (PDF, 211 KB).

[19]

O. Aichholzer, F. Aurenhammer, E.D. Demaine, F. Hurtado, P. Ramos, and J. Urrutia. On k-convex polygons. Computational Geometry: Theory and Applications, 45:73-87, 2012. (PDF, 225 KB).

[20]

O. Aichholzer, F. Aurenhammer, T. Hackl, B. Juettler, M. Oberneder, and Z. Sir. Computational and structural advantages of circular boundary representation. Int'l Journal of Computational Geometry & Applications, 21:47-69, 2011. (PDF, 267 KB).

[21]

O. Aichholzer, W. Aigner, F. Aurenhammer, K. Cech Dobiasova, B. Jüttler, and G. Rote. Triangulations with circular arcs. In Proc. 19th Int. Symposium on Graph Drawing, Springer LNCS, volume 7034, pages 296-307, Eindhoven, Netherlands, 2011. (PDF, 184 KB).

[22]

O. Aichholzer, W. Aigner, F. Aurenhammer, and B. Jüttler. Exact medial axis computation for triangulated solids with respect to piecewise linear metrics. In Proc. Int. Conf. Curves and Surfaces, Springer LNCS, volume 6920, pages 1-27, Avignon, France, 2011. (PDF, 958 KB).

[23]

M. Demuth, F. Aurenhammer, and A. Pinz. Straight skeletons for binary shapes. In 3rd Workshop on non-rigid shape analysis and deformable image alignment (NORDIA'10), San Francisco, USA, 2010. (PDF, 104 KB).

[24]

O. Aichholzer, F. Aurenhammer, T. Hackl, C. Huemer, A. Pilz, and B. Vogtenhuber. 3-colorability of pseudo-triangulations. In Proc. 26th European Workshop on Computational Geometry EuroCG'10, pages 21-24, Dortmund, Germany, 2010. (PDF, 109 KB).

[25]

O. Aichholzer, W. Aigner, F. Aurenhammer, K. Cech Dobiasova, B. Jüttler, and G. Rote. Arc triangulations. In Proc. 26th European Workshop on Computational Geometry EuroCG '2010, pages 17-20, Dortmund, Germany, 2010. (PDF, 168 KB).

[26]

O. Aichholzer, W. Aigner, F. Aurenhammer, T. Hackl, B. Jüttler, E. Pilgerstorfer, and M. Rabl. Divide-and conquer for Voronoi diagrams revisited. Computational Geometry: Theory and Applications, 43:688-699, 2010. (PDF, 719 KB).

[27]

B. Aronov, F. Aurenhammer, F. Hurtado, S. Langerman, D. Rappaport, S. Smorodinsky, and C. Seara. Small weak epsilon nets. Computational Geometry: Theory and Applications, 42:455-462, 2009. Special Issue. (PDF, 218 KB).

[28]

O. Aichholzer, F. Aurenhammer, O. Devillers, T. Hackl, M. Teillaud, and B. Vogtenhuber. Lower and upper bounds on the number of empty cylinders and ellipsoids. In Proc. 25th European Workshop on Computational Geometry EuroCG'09, pages 139-141, Brussels, Belgium, 2009. (PDF, 165 KB).

[29]

O. Aichholzer, F. Aurenhammer, F. Hurtado, P.A. Ramos, and J. Urrutia. Two-convex polygons. In Proc. 25th European Workshop on Computational Geometry EuroCG'09, pages 117-120, Brussels, Belgium, 2009. (PDF, 126 KB).

[30]

O. Aichholzer, F. Aurenhammer, T. Hackl, and B. Speckmann. On minimum weight pseudo-triangulations. Computational Geometry: Theory and Applications, 42:627-631, 2009. (PDF, 101 KB).

[31]

O. Aichholzer, F. Aurenhammer, B. Kornberger, S. Plantinga, G. Rote, A. Sturm, and G. Vegter. Recovering structure from r-sampled objects. In Eurographics Symposium on Geometry Processing, Computer Graphics Forum, volume 28, pages 1349-1360, Berlin, Germany, 2009. Special Issue. (PDF, 613 KB).

[32]

O. Aichholzer, W. Aigner, F. Aurenhammer, T. Hackl, B. Jüttler, E. Pilgerstorfer, and M. Rabl. Divide-and conquer for Voronoi diagrams revisited. In Proc. 25th Ann. ACM Symp. Computational Geometry, pages 189-197, Aarhus, Denmark, 2009. (PDF, 711 KB).

[33]

O. Aichholzer, W. Aigner, F. Aurenhammer, T. Hackl, B. Jüttler, E. Pilgerstorfer, and M. Rabl. Divide-and conquer for Voronoi diagrams revisited. In Proc. 25th European Workshop on Computational Geometry EuroCG'09, pages 293-296, Brussels, Belgium, 2009. (PDF, 145 KB).

[34]

O. Aichholzer, W. Aigner, F. Aurenhammer, T. Hackl, B. Juettler, and M. Rabl. Medial axis computation for planar free-form shapes. Computer Aided Design, 41:339-349, 2009. Special Issue. (PDF, 1221 KB).

[35]

F. Aurenhammer and Y.-F.Xu. Optimal triangulations. In Encyclopedia of Optimization, Second Edition, P.M.Pardalos C.A.Floudas, editor, pages 2757-2764. Springer, 2008. (PDF, 135 KB).

[36]

F. Aurenhammer, M. Demuth, and T. Schiffer. Computing convex quadrangulations. In Proc. 5th Ann. Int. Symp. Voronoi Diagrams in Science and Engineering, Voronoi's Impact on Modern Science, volume 4, pages 32-43, Kiev, Ukraine, 2008. (PDF, 95 KB).

[37]

O. Aichholzer, F. Aurenhammer, O. Devillers, T. Hackl, M. Teillaud, and B. Vogtenhueber. Counting quadrics and Delaunay triangulations and a new convex hull theorem. INRIA Report 6748, INRIA, Sofia Antipolis, France, 2008.

[38]

O. Aichholzer, F. Aurenhammer, P. Gonzalez-Nava, T. Hackl, C. Huemer, F. Hurtado, H. Krasser, S. Ray, and B. Vogtenhuber. Matching edges and faces in polygonal partitions. Computational Geometry: Theory and Applications, 39:134-141, 2008. (PDF, 88 KB).

[39]

O. Aichholzer, F. Aurenhammer, T. Hackl, B. Kornberger, S. Plantinga, G. Rote, A. Sturm, and G. Vegter. Seed polytopes for incremental approximation. In Proc. 24th European Workshop on Computational Geometry EuroCG '08, pages 13-16, Nancy, France, 2008. (PDF, 113 KB).

[40]

F. Aurenhammer, M. Peternell, H. Pottmann, and J. Wallner. Voronoi diagrams for oriented spheres. In Proc. 4th Int. Symp. on Voronoi Diagrams in Science and Engineering, ISVD'07, pages 33-37, Pontypridd, UK, 2007. (PDF, 81 KB).

[41]

F. Aurenhammer. Weighted skeletons and fixed-share decomposition. Computational Geometry: Theory and Applications, 40:93-101, 2007. (PDF, 101 KB).

[42]

O. Aichholzer, F. Aurenhammer, and T. Hackl. Pre-triangulations and liftable complexes. Discrete & Computational Geometry, 38:701-725, 2007. (PDF, 234 KB).

[43]

O. Aichholzer, F. Aurenhammer, T. Hackl, and C. Huemer. Connecting colored point sets. Discrete Applied Mathematics, 155:271-278, 2007. (PDF, 135 KB).

[44]

O. Aichholzer, F. Aurenhammer, T. Hackl, B. Juettler, M. Oberneder, and Z. Sir. Computational and structural advantages of circular boundary representation. In Proc. 10th Int. Workshop on Algorithms and Data Structures, WADS'07, Springer LNCS 4619, pages 374-385, Halifax, Canada, 2007. (PDF, 176 KB).

[45]

O. Aichholzer, F. Aurenhammer, T. Hackl, B. Kornberger, M. Peternell, and H. Pottmann. Approximating boundary-triangulated objects with balls. In Proc. 23rd European Workshop on Computational Geometry, EWCG'07, pages 130-133, Graz, Austria, 2007. (PDF, 147 KB).

[46]

O. Aichholzer, F. Aurenhammer, T. Hackl, and B. Speckmann. On (pointed) minimum weight pseudo-triangulations. In Proc. 19th Canadian Conference on Computational Geometry CCCG '07, pages 209-212, Ottawa, Canada, 2007. (PDF, 111 KB).

[47]

O. Aichholzer, F. Aurenhammer, C. Huemer, and B. Vogtenhuber. Gray code enumeration of plane straight-line graphs. Graphs and Combinatorics, 23:467-479, 2007. (PDF, 137 KB).

[48]

F. Aurenhammer and H. Krasser. Pseudo-simplicial complexes from maximal locally convex functions. Discrete & Computional Geometry, 35:201-221, 2006. (PDF, 277 KB).

[49]

F. Aurenhammer, R.L.S.Drysdale, and H. Krasser. Farthest line segment Voronoi diagrams. Information Processing Letters, 100:220-225, 2006. (PDF, 77 KB).

[50]

O. Aichholzer, F. Aurenhammer, and T. Hackl. Pre-triangulations and liftable complexes. In 22nd Ann. ACM Symp. Computational Geometry, pages 282-291, Sedona, Arizona, USA, 2006. (PDF, 225 KB).

[51]

O. Aichholzer, F. Aurenhammer, C. Huemer, and H. Krasser. Transforming spanning trees and pseudo-triangulations. Information Processing Letters, 97:19-22, 2006. (PDF, 91 KB).

[52]

O. Aichholzer, F. Aurenhammer, C. Huemer, and B. Vogtenhuber. Gray code enumeration of plane straight-line graphs. In Proc. 22nd European Workshop on Computational Geometry EuroCG '06, pages 71-74, Delphi, Greece, 2006. (PDF, 110 KB).

[53]

O. Aichholzer, F. Aurenhammer, and H. Krasser. On the crossing number of complete graphs. Computing, 76:165-176, 2006. (PDF, 232 KB).

[54]

F. Aurenhammer and H. Krasser. Pseudo-tetrahedral complexes. In Proc. 21st European Workshop on Computational Geometry EuroCG '05, pages 85-88, Eindhoven, The Netherlands, 2005. (PDF, 112 KB).

[55]

F. Aurenhammer. Pre-triangulations: A generalization of Delaunay triangulations and flips. In 2nd Intern. Symp. on Voronoi Diagrams in Science and Engineering, page 235, Hanyang University, Seoul, Korea, 2005. (plenar talk).

[56]

B. Aronov, F. Aurenhammer, F. Hurtado, S. Langerman, D. Rappaport, S. Smorodinsky, and C. Seara. Small weak epsilon nets. In Proc. 17th Canadian Conference on Computational Geometry CCCG '05, pages 51-54, Windsor, Ontario, 2005. (PDF, 180 KB).

[57]

O. Aichholzer, F. Aurenhammer, P. Gonzalez-Nava, T. Hackl, C. Huemer, F. Hurtado, H. Krasser, S. Ray, and B. Vogtenhuber. Matching edges and faces in polygonal partitions. In Proc. 17th Canadian Conference on Computational Geometry CCCG '05, pages 123-126, Windsor, Ontario, 2005. (PDF, 144 KB).

[58]

O. Aichholzer, F. Aurenhammer, C. Huemer, and H. Krasser. Transforming spanning trees and pseudo-triangulations. In Proc. 21st European Workshop on Computational Geometry EuroCG '05, pages 81-84, Eindhoven, The Netherlands, 2005. (PDF, 73 KB).

[59]

O. Aichholzer, F. Aurenhammer, H. Krasser, and B. Speckmann. Convexity minimizes pseudo-triangulations. Computational Geometry: Theory and Applications, 28:3-10, 2004. .

[60]

O. Aichholzer, F. Aurenhammer, and B. Palop. Quickest paths, straight skeletons, and the city Voronoi diagram. Discrete & Computational Geometry, 31(1):17-35, 2004. (PDF, 199 KB).

[61]

F. Aurenhammer. Pseudo-simplices and their derivation. In Voronoi Conference on Analytic Number Theory and Spatial Tesselations, page 11, Inst. Math. National Academy of Sciences, Kiev, Ukraine, 2003.

[62]

O. Aichholzer, F. Aurenhammer, P. Brass, and H. Krasser. Pseudo-triangulations from surfaces and a novel type of edge flip. SIAM Journal on Computing, 32:1621-1653, 2003. .

[63]

O. Aichholzer, F. Aurenhammer, P. Brass, and H. Krasser. Spatial embedding of pseudo-triangulations. In Proc. 19th Ann. ACM Symp. Computational Geometry, pages 144-153, San Diego, California, USA, 2003. .

[64]

O. Aichholzer, F. Aurenhammer, F. Hurtado, and H. Krasser. Towards compatible triangulations. Theoretical Computer Science, 296:3-13, 2003. Special Issue. (Gzipped PostScript, 13 p., 94 KB).

[65]

O. Aichholzer, F. Aurenhammer, and H. Krasser. Adapting (pseudo)-triangulations with a near-linear number of edge flips. In Lecture Notes in Computer Science 2748, Proc. 8th International Workshop on Algorithms and Data Structures (WADS), volume 2748, pages 12-24, 2003. .

[66]

F. Aurenhammer, N. Katoh, H. Kojima, M. Ohsaki, and Y.-F. Xu. Approximating uniform triangular meshes in polygons. Theoretical Computer Science, 289:879-895, 2002. Special Issue. [SFB Report F003-159, TU Graz, Austria, 1999]. (Gzipped PostScript, 14 p., 210 KB).

[67]

O. Aichholzer, F. Aurenhammer, and F. Hurtado. Sequences of spanning trees and a fixed tree theorem. Computational Geometry: Theory and Applications, 21(1-2):3-20, 2002. Special Issue. [Report MA2-IR-00-00026, Universitat Politecnica de Catalunya, Barcelona, Spain, 2000]. (Gzipped PostScript, 22 p., 117 KB). You can also download the nice program MST-Tool we used to check and visualize some of the presented results!

[68]

O. Aichholzer, F. Aurenhammer, and H. Krasser. On the crossing number of complete graphs. In Proc. 18th Ann. ACM Symp. Computational Geometry, pages 19-24, Barcelona, Spain, 2002. (PDF, 134 KB).

[69]

O. Aichholzer, F. Aurenhammer, and H. Krasser. On the crossing number of complete graphs - extended abstract. In Proc. 18th European Workshop on Computational Geometry CG '02, pages 90-92, Warszawa, Poland, 2002. (PDF, 71 KB).

[70]

O. Aichholzer, F. Aurenhammer, and H. Krasser. Enumerating order types for small point sets with applications. Order, 19:265-281, 2002. (Gzipped PostScript, 8 p., 70 KB). See also our order type homepage.

[71]

O. Aichholzer, F. Aurenhammer, and H. Krasser. Points and combinatorics. Special Issue on Foundations of Information Processing of TELEMATIK, 1:12-17, 2002. (Gzipped PostScript, 9 p., 74 KB).

[72]

O. Aichholzer, F. Aurenhammer, and H. Krasser. Progress on rectilinear crossing numbers. Technical report, IGI-TU Graz, Austria, 2002. (Gzipped PostScript, 8 p., 66 KB). See also our crossing number homepage.

[73]

O. Aichholzer, F. Aurenhammer, H. Krasser, and B. Speckmann. Convexity minimizes pseudo-triangulations. In Proc. 14th Annual Canadian Conference on Computational Geometry CCCG 2002, pages 158-161, Lethbridge, Alberta, Canada, 2002. .

[74]

O. Aichholzer, F. Aurenhammer, and B. Palop. Quickest paths, straight skeletons, and the city Voronoi diagram. In Proc. 18th Ann. ACM Symp. Computational Geometry, pages 151-159, Barcelona, Spain, 2002. .

[75]

O. Aichholzer, F. Aurenhammer, and T. Werner. Algorithmic fun - Abalone. Special Issue on Foundations of Information Processing of TELEMATIK, 1:4-6, 2002. (Gzipped PostScript, 5 p., 420 KB).

[76]

O. Aichholzer and F. Aurenhammer. Voronoi diagrams - computational geometry's favorite. Special Issue on Foundations of Information Processing of TELEMATIK, 1:7-11, 2002. (Gzipped PostScript, 7 p., 189 KB).

[77]

F. Aurenhammer. Computational geometry -- some easy questions and their recent solutions. J. Universal Computer Science, 7:338-354, 2001. Special Issue. (Gzipped PostScript, 17 p., 98 KB).

[78]

O. Aichholzer, F. Aurenhammer, B. Brandtstaetter, H. Krasser, C. Magele, M. Muehlmann, and W. Renhart. Evolution trategy and ierarchical lustering. In 13th COMPUMAG Conference on the Computation of Electromagnetic Fields, Lyon-Evian, France, 2001. (Gzipped PostScript, 2 p., 253 KB).

[79]

O. Aichholzer, F. Aurenhammer, F. Hurtado, and H. Krasser. Towards compatible triangulations. In Proc. 7th Ann. Int'l. Computing and Combinatorics Conf. COCOON'01, Lecture Notes in Computer Science, Jie Wang, editor, volume 2108, pages 101-110, Guilin, China, 2001. Springer Verlag. (Gzipped PostScript, 10 p., 75 KB).

[80]

O. Aichholzer, F. Aurenhammer, C. Icking, R. Klein, E. Langetepe, and G. Rote. Generalized self-approaching curves. Discrete Applied Mathematics, 109(1-2):3-24, 2001. Special Issue. [SFB-Report F003-134, TU Graz, Austria, 1998]. (Gzipped PostScript, 21 p., 193 KB). (PDF, 385 KB).

[81]

O. Aichholzer, F. Aurenhammer, and H. Krasser. On compatible triangulations of point sets. In Proc. 17th European Workshop on Computational Geometry CG '2001, pages 23-26, Berlin, Germany, 2001. (Gzipped PostScript, 4 p., 42 KB).

[82]

O. Aichholzer, F. Aurenhammer, and H. Krasser. Enumerating order types for small point sets with applications. In Proc. 17th Ann. ACM Symp. Computational Geometry, pages 11-18, Medford, Massachusetts, USA, 2001. (Gzipped PostScript, 8 p., 70 KB).

[83]

F. Aurenhammer and Y.-F.Xu. Optimal triangulations. In Encyclopedia of Optimization, P.M.Pardalos C.A.Floudas, editor, volume 4, pages 160-166. Kluwer Academic Publishing, 2000. [SFB Report F003-099, Tu Graz, Austria, 1998]. (Gzipped PostScript, 8 p., 75 KB).

[84]

F. Aurenhammer and R. Klein. Voronoi diagrams. In Handbook of Computational Geometry, Chapter V, J. Sack and G. Urrutia, editors, pages 201-290. Elsevier Science Publishing, 2000. [SFB Report F003-092, TU Graz, Austria, 1996]. (Gzipped PostScript, 101 p., 473 KB).

[85]

F. Aurenhammer, N. Katoh, H. Kojima, M. Ohsaki, and Y.-F. Xu. Approximating uniform triangular meshes in polygons. In Proc. 6th Ann. Intl. Computing and Combinatorics Conference, Lecture Notes in Computer Science, volume 1558, pages 23-33, Sydney, Australia, 2000. Springer Verlag. (PDF, 252 KB).

[86]

O. Aichholzer, F. Aurenhammer, B. Brandtstaetter, T. Ebner, H. Krasser, and C. Magele. Niching evolution strategy with cluster algorithms. In 9th Biennial IEEE Conf. Electromagnetic Field Computations, Milwaukee, Wisconsin, USA, 2000. (Gzipped PostScript, 4 p., 334 KB).

[87]

O. Aichholzer, F. Aurenhammer, and F. Hurtado. Edge operations on non-crossing spanning trees. In Proc. 16th European Workshop on Computational Geometry CG '2000, pages 121-125, Eilat, Israel, 2000. (PDF, 143 KB).

[88]

O. Aichholzer, F. Aurenhammer, D.Z. Chen, D.T. Lee, and E. Papadopoulou. Skew Voronoi diagrams. Int'l. Journal of Computational Geometry & Applications, 9:235-247, 1999. (Gzipped PostScript, 13 p., 86 KB). Click here for Figures and Animations of Skew Voronoi Diagrams

[89]

O. Aichholzer, F. Aurenhammer, and R. Hainz. New results on MWT subgraphs. Information Processing Letters, 69:215-219, 1999. [SFB Report F003-140, TU Graz, Austria, 1998]. (Gzipped PostScript, 7 p., 60 KB).

[90]

O. Aichholzer, F. Aurenhammer, G. Rote, and Y.-F. Xu. Constant-level greedy triangulations approximate the MWT well. Journal of Combinatorial Optimization, 2:361-369, 1999. [SFB-Report F003-050, TU Graz, Austria, 1995]. (Gzipped PostScript, 9 p., 90 KB).

[91]

F. Aurenhammer, F. Hoffmann, and B. Aronov. Minkowski-type theorems and least-squares clustering. Algorithmica, 20:61-76, 1998. [SFB Report F003-075, TU Graz, Austria, 1996]. (Gzipped PostScript, 17 p., 93 KB).

[92]

O. Aichholzer, F. Aurenhammer, C. Icking, R. Klein, E. Langetepe, and G. Rote. Generalized self-approaching curves. In Proc. 14th European Workshop on Computational Geometry CG '98, pages 15-18, Barcelona, Spain, 1998. (Gzipped PostScript, 3 p., 91 KB).

[93]

O. Aichholzer, F. Aurenhammer, C. Icking, R. Klein, E. Langetepe, and G. Rote. Generalized self-approaching curves. In Proc. 9th Int. Symp. Algorithms and Computation ISAAC'98, Lecture Notes in Computer Science, volume 1533, pages 317-326, Taejon, Korea, 1998. Springer Verlag. (Gzipped PostScript, 10 p., 169 KB).

[94]

O. Aichholzer and F. Aurenhammer. Straight skeletons for general polygonal figures in the plane. In Voronoi's Impact on Modern Sciences II, A.M. Samoilenko, editor, volume 21, pages 7-21. Proc. Institute of Mathematics of the National Academy of Sciences of Ukraine, Kiev, Ukraine, 1998. (Gzipped PostScript, 14 p., 92 KB).

[95]

R. Hainz, O. Aichholzer, and F. Aurenhammer. New results on minimum-weight triangulations and the LMT skeleton. In Proc. 13th European Workshop on Computational Geometry CG '97, pages 4-6, Wuerzburg, Germany, 1997. (Gzipped PostScript, 3 p., 69 KB).

[96]

O. Aichholzer, F. Aurenhammer, D.Z. Chen, D.T. Lee, A. Mukhopadhyay, and E. Papadopoulou. Voronoi diagrams for direction-sensitive distances (communication). In Proc. 13th Ann. ACM Symp. Computational Geometry, pages 418-420, Nice, France, 1997. [SFB Report F003-098, TU Graz, Austria, 1996]. (Gzipped PostScript, 3 p., 52 KB).

[97]

O. Aichholzer, F. Aurenhammer, S.-W. Cheng, N. Katoh, G. Rote, M. Taschwer, and Y.-F. Xu. Triangulations intersect nicely. Discrete & Computational Geometry, 16:339-359, 1996. Special Issue. [SFB Report F003-030, TU Graz, Austria, 1995]. (Gzipped PostScript, 20 p., 116 KB).

[98]

O. Aichholzer, F. Aurenhammer, G. Rote, and Y.-F. Xu. Constant-level greedy triangulations approximate the MWT well. In Proc. 2nd Int'l. Symp. Operations Research & Applications ISORA'96, Lecture Notes in Operations Research, Cheng Du, Zhang, editor, volume 2, pages 309-318, Guilin, P. R. China, 1996. World Publishing Corporation. (Gzipped PostScript, 10 p., 60 KB).

[99]

O. Aichholzer, F. Aurenhammer, G. Rote, and Y.-F. Xu. New greedy triangulation algorithms. In Proc. 12th European Workshop on Computational Geometry CG '96, pages 11-14, Muenster, Germany, 1996. (Gzipped PostScript, 4 p., 55 KB).

[100]

O. Aichholzer and F. Aurenhammer. Classifying hyperplanes in hypercubes. SIAM Journal on Discrete Mathematics, 9(2):225-232, 1996. [IIG-Report-Series 408, TU Graz, Austria, 1995]. (Gzipped PostScript, 12 p., 73 KB).

[101]

O. Aichholzer and F. Aurenhammer. Straight skeletons for general polygonal figures. In Proc. 2nd Ann. Int'l. Computing and Combinatorics Conf. COCOON'96, Lecture Notes in Computer Science, volume 1090, pages 117-126, Hong Kong, 1996. Springer Verlag. [IIG-Report-Series 423, TU Graz, Austria, 1995]. (Gzipped PostScript, 11 p., 57 KB).

[102]

F. Aurenhammer and J. Hagauer. Recognizing binary Hamming graphs in O(n2 log n) time. Mathematical Systems Theory, 28:387-395, 1995. [IIG-Report-Series 273, TU Graz, Austria, 1989]. (Gzipped PostScript, 11 p., 56 KB).

[103]

F. Aurenhammer. Guest editor's foreword of the special issue on computational geometry. Int'l Journal of Computational Geometry & Applications, 5:1, 1995.

[104]

O. Aichholzer, F. Aurenhammer, and G. Rote. Optimal graph orientation with storage applications. SFB-Report F003-51, SFB 'Optimierung und Kontrolle', TU Graz, Austria, 1995. (Gzipped PostScript, 7 p., 59 KB).

[105]

O. Aichholzer, F. Aurenhammer, G. Rote, and M. Taschwer. Triangulations intersect nicely. In Proc. 11th Ann. ACM Symp. Computational Geometry, pages 220-229, Vancouver, Canada, 1995. (Gzipped PostScript, 10 p., 87 KB).

[106]

O. Aichholzer, D. Alberts, F. Aurenhammer, and B. Gaertner. A novel type of skeleton for polygons. Journal of Universal Computer Science, 1(12):752-761, 1995. [IIG-Report-Series 424, TU Graz, Austria, 1995]. (Gzipped PostScript, 9 p., 63 KB). Click here for the Online Version

[107]

O. Aichholzer, D. Alberts, F. Aurenhammer, and B. Gaertner. Straight skeletons of simple polygons. In Proc. 4th Int. Symp. of LIESMARS, pages 114-124, Wuhan, P. R. China, 1995. (Gzipped PostScript, 11 p., 49 KB).

[108]

F. Aurenhammer, M. Formann, R. Idury, A. Schaeffer, and F. Wagner. Faster isometric embedding in products of complete graphs. Discrete Applied Mathematics, 52:17-28, 1994. [Report B-90-06, FU Berlin, Germany, 1990]. (Gzipped PostScript, 13 p., 76 KB).

[109]

O. Aichholzer and F. Aurenhammer. Classifying hyperplanes in hypercubes. In Proc. 10th European Workshop on Computational Geometry CG '94, pages 53-57, Santander, Spain, 1994. (Gzipped PostScript, 5 p., 43 KB).

[110]

F. Aurenhammer. Geometric clustering and Voronoi-type partitions. In 16th IFIP Conf. System Modelling and Optimization, pages 93-94, Compiegne, France, 1993.

[111]

F. Aurenhammer. Voronoi diagrams -- a survey of a fundamental geometric data structure. bit acm computing surveys '91 (Japanese translation), Kyoritsu Shuppan Co., Ltd., pages 131-185, 1993.

[112]

F. Aurenhammer and G. Stoeckl. Searching for segments with largest relative overlap. In Proc. 15th IFIP Conf. System Modelling and Optimization, Lecture Notes in Control and Information Sciences, volume 180, pages 77-84, Zuerich, Switzerland, 1992. Springer Verlag.

[113]

F. Aurenhammer and G. Stoeckl. Searching for segments with largest relative overlap. Information Processing Letters, 41:103-108, 1992. [Report B 91-10, FU Berlin, Germany, 1991].

[114]

F. Aurenhammer and O. Schwarzkopf. A simple on-line randomized incremental algorithm for computing higher order Voronoi diagrams. Int'l Journal of Computational Geometry & Applications, 2:363-381, 1992. Special Issue. [Report B 91-02, FU Berlin, Germany, 1991]. (Gzipped PostScript, 18 p., 92 KB).

[115]

F. Aurenhammer, F. Hoffmann, and B. Aronov. Least-squares partitioning. In Proc. 8th European Workshop on Computational Geometry CG '92, pages 55-57, Utrecht, the Netherlands, 1992.

[116]

F. Aurenhammer, F. Hoffmann, and B. Aronov. Minkowski-type theorems and least-squares partitioning. In Proc. 8th Ann. ACM Symp. Computational Geometry, pages 350-357, Berlin, Germany, 1992. [Report B-92-09, FU Berlin, Germany, 1992].

[117]

F. Aurenhammer, J. Hagauer, and W. Imrich. Cartesian graph factorization at logarithmic cost per edge. Computational Complexity, 2:331-349, 1992.

[118]

F. Aurenhammer and J. Hagauer. Computing equivalence classes among the edges of a graph with applications. Discrete Mathematics, 109:3-12, 1992. Special Issue. [IIG-Report-Series 271, TU Graz, Austria, 1989].

[119]

F. Aurenhammer, G. Stoeckl, and E. Welzl. The post-office problem for fuzzy point sets. In Proc. 7th Workshop on Computational Geometry CG '91, Lecture Notes in Computer Science, volume 553, pages 1-11, Bern, Switzerland, 1991. Springer Verlag. [Report B 91-07, FU Berlin, Germany, 1991].

[120]

F. Aurenhammer and G. Stoeckl. On the peeper's Voronoi diagram. SIGACT News, 22(4):50-59, 1991. [IIG-Report-Series 264, TU Graz, Austria, 1988]. (Gzipped PostScript, 10 p., 64 KB).

[121]

F. Aurenhammer and O. Schwarzkopf. A simple on-line randomized incremental algorithm for computing higher order Voronoi diagrams. In Proc. 7th Ann. ACM Symp. Computational Geometry, pages 142-151, North Conway, U.S.A., 1991.

[122]

F. Aurenhammer and J. Hagauer. Recognizing binary Hamming graphs in O(n2 log n) time. In Proc. 16th Int'l Workshop on Graph-Theoretical Concepts in Computer Science, Lecture Notes in Computer Science, volume 484, pages 90-98, Berlin, Germany, 1991. Springer Verlag.

[123]

F. Aurenhammer. Using Gale transforms in computational geometry. Mathematical Programming, B 52:179-190, 1991. Special Issue. [IIG-Report-Series 248, TU Graz, Austria, 1988].

[124]

F. Aurenhammer. Voronoi diagrams -- a survey of a fundamental geometric data structure. ACM Computing Surveys, 23(3):345-405, 1991. Habilitationsschrift. [Report B 90-09, FU Berlin, Germany, 1990].

[125]

F. Aurenhammer and G. Stoeckl. Fenster - Voronoi Diagramme (Abstract). In Tagungsband DMV Jubilaeumstagung, page 52, Bremen, Germany, 1990.

[126]

F. Aurenhammer, J. Hagauer, and W. Imrich. Factoring Cartesian-product graphs at logarithmic cost per edge. In Proc. MPS Conf. Integer Programming and Combinatorial Optimization IPCO'90, pages 29-44, Waterloo, Canada, 1990. [IIG-Report-Series 287, TU Graz, Austria, 1990].

[127]

F. Aurenhammer. A new duality result concerning Voronoi diagrams. Discrete & Computational Geometry, 5(3):243-254, 1990. [IIG-Report-Series 216, TU Graz, Austria, 1985].

[128]

F. Aurenhammer. A relationship between Gale transforms and Voronoi diagrams. Discrete Applied Mathematics, 28:83-91, 1990. [IIG-Report-Series 247, TU Graz, Austria, 1988].

[129]

F. Aurenhammer and J. Hagauer. Computing equivalence classes among the edges of a graph with applications. In Proc. Int'l Conf. Algebraic Graph Theory, page 11, Leibnitz, Austria, 1989.

[130]

F. Aurenhammer and H. Imai. Geometric relations among Voronoi diagrams. Geometriae Dedicata, 27:65-75, 1988. [IIG-Report-Series 228, TU Graz, Austria, 1986].

[131]

F. Aurenhammer. Algorithmic aspects of Gale transforms (abstract). In Proc. 13th 3-Ann. Int'l Symp. Mathematical Programming, page 176, Tokyo, Japan, 1988.

[132]

F. Aurenhammer. Improved algorithms for discs and balls using power diagrams. Journal of Algorithms, 9(2):151-161, 1988. [IIG-Report-Series 209, TU Graz, Austria, 1985].

[133]

F. Aurenhammer. Linear combinations from power domains. Geometriae Dedicata, 28:45-52, 1988. [IIG-Report-Series 243, TU Graz, Austria, 1987].

[134]

F. Aurenhammer. On-line sorting of twisted sequences in linear time. BIT, 28:194-204, 1988. [IIG-Report-Series 232, TU Graz, Austria, 1987].

[135]

F. Aurenhammer. On-line sorting of twisted sequences in linear time. In 2nd Workshop on Computational Geometry and Discrete Algorithms, Osaka, Japan, 1988.

[136]

F. Aurenhammer. Using Gale transforms in computational geometry. In Proc. 4th Workshop on Computational Geometry CG '88, Lecture Notes in Computer Science, volume 333, pages 202-216, Wuerzburg, Germany, 1988. Springer Verlag.

[137]

F. Aurenhammer and H. Imai. Geometric relations among Voronoi diagrams. In Proc. 4th Ann. STACS, Lecture Notes in Computer Science, volume 247, pages 53-65, Passau, Germany, 1987. Springer Verlag.

[138]

F. Aurenhammer. A criterion for the affine equivalence of cell complexes in Rd and convex polyhedra in Rd+1. Discrete & Computational Geometry, 2(1):49-64, 1987. [IIG-Report-Series 205, TU Graz, Austria, 1985].

[139]

F. Aurenhammer. Jordan sorting via convex hulls of certain non-simple polygons. In Proc. 3rd Ann. ACM Symp. Computational Geometry, pages 21-29, Waterloo, Canada, 1987.

[140]

F. Aurenhammer. Power diagrams: properties, algorithms, and applications. SIAM Journal on Computing, 16(1):78-96, 1987. [IIG-Report-Series F120, TU Graz, Austria, 1983].

[141]

F. Aurenhammer. Recognizing polytopical cell complexes and constructing projection polyhedra. Journal of Symbolic Computation, 3(3):249-255, 1987. [IIG-Report-Series 203, TU Graz, Austria, 1985].

[142]

F. Aurenhammer. A new duality result concerning Voronoi diagrams. In Proc. 13th Ann. ICALP, Lecture Notes in Computer Science, volume 226, pages 21-32, Rennes, France, 1986. Springer Verlag.

[143]

F. Aurenhammer. The one-dimensional weighted Voronoi diagram. Information Processing Letters, 22(3):119-123, 1986. [IIG-Report-Series F110, TU Graz, Austria, 1983].

[144]

F. Aurenhammer. Gewichtete Voronoidiagramme. In Workshop on Computational Geometry CG '85, Karlsruhe, Germany, 1985.

[145]

F. Aurenhammer and H. Edelsbrunner. An optimal algorithm for constructing the weighted Voronoi diagram in the plane. Pattern Recognition, 17(2):251-257, 1984. [IIG-Report-Series F109, TU Graz, Austria, 1983].

[146]

F. Aurenhammer. Gewichtete Voronoi Diagramme: Geometrische Deutung und Konstruktions-Algorithmen. PhD thesis, IIG-TU Graz, Austria, 1984. Report B53.

[147]

F. Aurenhammer. On the generality of power diagrams. IIG Report F126, TU Graz, Austria, 1983.

 

Contact
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Prof. Dr. Franz Aurenhammer
Institute for Theoretical Computer Science
Inffeldgasse 16b/I
8010 Graz
Austria

Phone:  +43 316 / 873 - 5844
Fax:        +43 316 / 873 - 105844
franz.aurenhammernoSpam@igi.tugraz.at