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Oswin Aichholzer's Publications

This list is also available as BiBTeX file.

[1]
O. Aichholzer, T. Hackl, C. Huemer, F. Hurtado, and B. Vogtenhuber. Large bichromatic point sets admit empty monochromatic 4-gons. SIAM Journal on Discrete Mathematics (SIDMA), 23(9):2147-2155, 2010.

[2]
O. Aichholzer, S. Cabello, R. Fabila-Monroy, D. Flores-Peñaloza, T. Hackl, C. Huemer, F. Hurtado, and D.R. Wood. Edge-removal and non-crossing configurations in geometric graphs. Discrete Mathematics & Theoretical Computer Science (DMTCS), page to appear, 2010.

[3]
O. Aichholzer, F. Aurenhammer, T. Hackl, B. Jüttler, M.Oberneder, and Z. Sír. Computational and structural advantages of circular boundary representation. Int'l. Journal of Computational Geometry & Applications, page to appear, 2010. Special Issue.

[4]
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, page to appear, 2010. (PDF, 1167352 bytes).

[5]
O. Aichholzer, T. Hackl, M. Hoffmann, C. Huemer, F. Santos, B. Speckmann, and B. Vogtenhuber. Maximizing maximal angles for plane straight line graphs. submitted to journal, 2009.

[6]
O. Aichholzer, T. Hackl, M. Hoffmann, A. Pilz, G. Rote, B. Speckmann, and B. Vogtenhuber. Plane graphs with parity constraints. In Lecture Notes in Computer Science, Proc. 11th International Workshop on Algorithms and Data Structures (WADS), volume 5664, pages 13-24, Banff, Alberta, Canada, 2009. .

[7]
O. Aichholzer, T. Hackl, C. Huemer, F. Hurtado, and B. Vogtenhuber. Large bichromatic point sets admit empty monochromatic 4-gons. In Proc. 25th European Workshop on Computational Geometry EuroCG '09, pages 133-136, Brussels, Belgium, 2009. (PDF, 131721 bytes).

[8]
O. Aichholzer, T. Hackl, D. Orden, P. Ramos, G. Rote, A. Schulz, and B. Speckmann. Flip graphs of bounded-degree triangulations. In Electronic Notes in Discrete Mathematics: Proc. European Conference on Combinatorics, Graph Theory and Applications EuroComb 2009, volume 34, pages 509-513, Bordeaux, France, 2009.

[9]
O. Aichholzer, J. García, D. Orden, and P.A. Ramos. New results on lower bounds for the number of ( leq k)-facets. European Journal of Combinatorics, 30:1568-1574, 2009. (PostScript, 244556 bytes).

[10]
O. Aichholzer, R. Fabila-Monroy, D. Flores-Peñaloza, T. Hackl, C. Huemer, and J. Urrutia. Empty monochromatic triangles. Computational Geometry: Theory and Applications, 42(9):934-938, 2009.

[11]
O. Aichholzer, R. Fabila-Monroy, D. Flores-Peñaloza, T. Hackl, C. Huemer, J. Urrutia, and B. Vogtenhuber. Modem illumination of monotone polygons. In Proc. 25th European Workshop on Computational Geometry EuroCG '09, pages 167-170, Brussels, Belgium, 2009. (PDF, 99624 bytes).

[12]
O. Aichholzer, S. Bereg, A. Dumitrescu, A. García, C. Huemer, F. Hurtado, M. Kano, A. Márquez, D. Rappaport, S. Smorodinsky, D. Souvaine, J. Urrutia, and D. Wood. Compatible geometric matchings. Computational Geometry: Theory and Applications, 42(6-7):617-626, 2009. (PDF, 148060 bytes).

[13]
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, special issue of Computer Graphics Forum 28(5), pages 1349-1360, Berlin, Germany, 2009. (PDF, 613494 bytes).

[14]
O. Aichholzer, F. Aurenhammer, T. Hackl, and B. Speckmann. On minimum weight pseudo-triangulations. Computational Geometry: Theory and Applications, 42(6-7):627-631, 2009. (PDF, 101244 bytes).

[15]
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 139-142, Brussels, Belgium, 2009. (PDF, 211170 bytes). Also available as Research Report RR-6748 "Counting Quadrics and Delaunay Triangulations and a new Convex Hull Theorem", INRIA, 2008, at http://hal.inria.fr/inria-00343651.

[16]
O. Aichholzer, F. Aurenhammer, F. Hurtado, P. Ramos, and J. Urrutia. Two-convex polygons. In Proc. 25th European Workshop on Computational Geometry EuroCG '09, pages 117-120, Brussels, Belgium, 2009. (PDF, 127314 bytes).

[17]
O. Aichholzer, W. Aigner, F. Aurenhammer, T. Hackl, B. Jüttler, and M. Rabl. Medial axis computation for planar free-form shapes. Computer-Aided Design, 41(5):339-349, 2009. Special issue: Voronoi Diagrams and their Applications. .

[18]
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, 145028 bytes).

[19]
O. Aichholzer, W. Aigner, F. Aurenhammer, T. Hackl, B. Jüttler, E. Pilgerstorfer, and M. Rabl. Divide-and-conquer for voronoi diagrams revisited. In 25th Ann. ACM Symp. Computational Geometry, pages 189-197, Aarhus, Denmark, 2009. (PDF, 1167352 bytes).

[20]
O. Aichholzer. [Empty] [colored] k-gons - Recent results on some Erdös-Szekeres type problems. In Proc. XIII Encuentros de Geometría Computacional, pages 43-52, Zaragoza, Spain, 2009. (PDF, 158554 bytes).

[21]
E. Ackerman, O. Aichholzer, and B. Keszegh. Improved upper bounds on the reflexivity of point sets. Computational Geometry: Theory and Applications, 42:241-249, 2009. (PDF, 233671 bytes).

[22]
O. Aichholzer, D. Orden, F. Santos, and B. Speckmann. On the number of pseudo-triangulations of certain point sets. Journal of Combinatorial Theory, Series A, 115(2):254-278, 2008. (PDF, 320282 bytes).

[23]
O. Aichholzer, C. Huemer, and H. Krasser. Triangulations without pointed spanning trees. Computational Geometry: Theory and Applications, 40(1):79-83, 2008. (PDF, 106150 bytes).

[24]
O. Aichholzer, R. Fabila-Monroy, D. Flores-Peñaloza, T. Hackl, C. Huemer, and J. Urrutia. Empty monochromatic triangles. In Proc. 20th Annual Canadian Conference on Computational Geometry CCCG 2008, pages 75-78, Montreal, Quebec, Canada, 2008. (PDF, 123429 bytes).

[25]
O. Aichholzer, S. Cabello, R. Fabila-Monroy, D. Flores-Peñaloza, T. Hackl, C. Huemer, F. Hurtado, and D.R. Wood. Edge-removal and non-crossing configurations in geometric graphs. In Proc. 24th European Workshop on Computational Geometry EuroCG '08, pages 119-122, Nancy, France, 2008. .

[26]
O. Aichholzer, S. Bereg, A. Dumitrescu, A. García, C. Huemer, F. Hurtado, M. Kano, A. Márquez, D. Rappaport, S. Smorodinsky, D. Souvaine, J. Urrutia, and D. Wood. Compatible geometric matchings. In Proc. 1st Topological & Geometric Graph Theory 2008, pages 194-199, Paris, France, 2008. (PostScript, 148060 bytes).

[27]
O. Aichholzer, S. Bereg, A. Dumitrescu, A. García, C. Huemer, F. Hurtado, M. Kano, A. Márquez, D. Rappaport, S. Smorodinsky, D. Souvaine, J. Urrutia, and D. Wood. Compatible geometric matchings. Electronic Notes in Discrete Mathematics, 31:201-206, 2008. (PDF, 148060 bytes). http://dx.doi.org/10.1016/j.endm.2008.06.040

[28]
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(2):134-141, 2008. (Gzipped PostScript, 10 pages, 62603 bytes).

[29]
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. .

[30]
O. Aichholzer, G. Rote, A. Schulz, and B. Vogtenhuber. Pointed drawings of planar graphs. In Proc. 19th Annual Canadian Conference on Computational Geometry CCCG 2007, pages 237-240, Ottawa, Ontario, Canada, 2007. (PDF, 157146 bytes).

[31]
O. Aichholzer and K. Reinhardt. A quadratic distance bound on sliding between crossing-free spanning trees. Computational Geometry: Theory and Applications, special issue, 37:155-161, 2007. (Gzipped PostScript, 10 pages, 138989 bytes).

[32]
O. Aichholzer, C. Huemer, S. Kappes, B. Speckmann, and C. D. Tóth. Decompositions, partitions, and coverings with convex polygons and pseudo-triangles. Graphs and Combinatorics, 23(5):481-507, 2007. (PDF, 449633 bytes).

[33]
O. Aichholzer, T. Hackl, C. Huemer, F. Hurtado, H. Krasser, and B. Vogtenhuber. On the number of plane geometric graphs. Graphs and Combinatorics (Springer), 23(1):67-84, 2007. (Gzipped PostScript, 16 pages, 238847 bytes).

[34]
O. Aichholzer, T. Hackl, M. Hoffmann, C. Huemer, F. Santos, B. Speckmann, and B. Vogtenhuber. Maximizing maximal angles for plane straight line graphs. In Proc. 23rd European Workshop on Computational Geometry EuroCG '07, pages 98-101, Graz, Austria, 2007. (PDF, 190360 bytes). Also available as FSP-report S092-48, Austria, 2007, at http://www.ig.jku.at/cgi-bin/CGI/Reports.pl.

[35]
O. Aichholzer, T. Hackl, M. Hoffmann, C. Huemer, A. Por, F. Santos, B. Speckmann, and B. Vogtenhuber. Maximizing maximal angles for plane straight line graphs. In Lecture Notes in Computer Science, Proc. 10th International Workshop on Algorithms and Data Structures (WADS), volume 4619, pages 458-469, Halifax, Nova Scotia, Canada, 2007. (PDF, 426080 bytes).

[36]
O. Aichholzer and T. Hackl, editors. Collection of Abstracts of the 23rd European Workshop on Computational Geometry 2007, Graz, Austria, 2007. Available at the conference homepage http://ewcg07.tugraz.at/EuroCG2007Abstracts.pdf.

[37]
O. Aichholzer, J. García, D. Orden, and P.A. Ramos. New lower bounds for the number of ( leq k)-edges and the rectilinear crossing number of kn. Discrete & Computational Geometry, 38:1-14, 2007. (Gzipped PostScript, 14 pages, 192371 bytes). Also available as FSP-report S092-20, Austria, 2006, at http://www.ig.jku.at/cgi-bin/CGI/Reports.pl.

[38]
O. Aichholzer, J. García, D. Orden, and P.A. Ramos. New results on lower bounds for the number of ( leq k)-facets. In Proceedings EuroComb'07, Electronic Notes in Discrete Mathematics, volume 29C, pages 189-193, 2007. (PostScript, 244556 bytes).

[39]
O. Aichholzer, F. Aurenhammer, T. Hackl, and C. Huemer. Connecting colored point sets. Discrete Applied Mathematics, 155(3):271-278, 2007. (Gzipped PostScript, 9 pages, 94471 bytes). Also available as FSP-report S092-45, Austria, 2006, at http://www.ig.jku.at/cgi-bin/CGI/Reports.pl.

[40]
O. Aichholzer, F. Aurenhammer, and T. Hackl. Pre-triangulations and liftable complexes. Discrete & Computational Geometry, 38:701-725, 2007. (Gzipped PostScript, 25 pages, 175458 bytes).

[41]
O. Aichholzer, F. Aurenhammer, C. Huemer, and B. Vogtenhuber. Gray code enumeration of plane straight-line graphs. Graphs and Combinatorics (Springer), 23(5):467-479, 2007. (PostScript, 139344 bytes).

[42]
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 EuroCG '07, pages 130-133, Graz, Austria, 2007. (PDF, 191559 bytes). Also available as FSP-report S092-49, Austria, 2007, at http://www.ig.jku.at/cgi-bin/CGI/Reports.pl.

[43]
O. Aichholzer, F. Aurenhammer, T. Hackl, B. Jüttler, M.Oberneder, and Z. Sír. Computational and structural advantages of circular boundary representation. In Lecture Notes in Computer Science, Proc. 10th International Workshop on Algorithms and Data Structures (WADS), volume 4619, pages 374-385, Halifax, Nova Scotia, Canada, 2007. (Gzipped PostScript, 17 pages, 119734 bytes). Also available as FSP-report S092-38, Austria, 2006, at http://www.ig.jku.at/cgi-bin/CGI/Reports.pl.

[44]
O. Aichholzer, F. Aurenhammer, T. Hackl, and B. Speckmann. On (pointed) minimum weight pseudo-triangulations. In Proc. 19th Annual Canadian Conference on Computational Geometry CCCG 2007, pages 209-212, Ottawa, Ontario, Canada, 2007. (PDF, 111677 bytes).

[45]
E. Ackerman, O. Aichholzer, and B. Keszegh. Improved upper bounds on the reflexivity of point sets. In Proc. 19th Annual Canadian Conference on Computational Geometry CCCG 2007, pages 29-32, Ottawa, Ontario, Canada, 2007. (PDF, 142630 bytes).

[46]
O. Aichholzer, D. Orden, and P.A. Ramos. On the structure of sets attaining the rectilinear crossing number. In Proc. 22nd European Workshop on Computational Geometry EuroCG '06, pages 43-46, Delphi, Greece, 2006. (PostScript, 193389 bytes).

[47]
O. Aichholzer and H. Krasser. Abstract order type extension and new results on the rectilinear crossing number. Computational Geometry: Theory and Applications, Special Issue on the 21st European Workshop on Computational Geometry, 36(1):2-15, 2006. (Gzipped PostScript, 18 pages, 155231 bytes).

[48]
O. Aichholzer, C. Huemer, S. Renkl, B. Speckmann, and C. D. Tóth. Decompositions, partitions, and coverings with convex polygons and pseudo-triangles. In Pawel Urzyczyn Rastislav Královic, editor, Proceedings 31st International Symposium on Mathematical Foundations of Computer Science, Lecture Notes in Computer Science, volume 4162, pages 86-97, Stará Lesná, Slovakia, 2006. (PDF, 202707 bytes).

[49]
O. Aichholzer, T. Hackl, C. Huemer, F. Hurtado, H. Krasser, and B. Vogtenhuber. On the number of plane graphs. In Proc. 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 504-513, Miami, Florida, USA, 2006. (PDF, 198074 bytes). Also available as FSP-report S092-8, Austria, 2006, at http://www.ig.jku.at/cgi-bin/CGI/Reports.pl.

[50]
O. Aichholzer, J. García, D. Orden, and P.A. Ramos. New lower bounds for the number of ( leq k)-edges and the rectilinear crossing number of kn. In Actas de las IV Jornadas de Matematica Discreta y Algoritmica, pages 57-64, 2006. (Gzipped PostScript, 14 pages, 192371 bytes).

[51]
O. Aichholzer, F. Aurenhammer, and H. Krasser. On the crossing number of complete graphs. Computing, 76:165-176, 2006. (Gzipped PostScript, 15 pages, 95316 bytes).

[52]
O. Aichholzer, F. Aurenhammer, C. Huemer, and H. Krasser. Transforming spanning trees and pseudo-triangulations. Information Processing Letters (IPL), 97(1):19-22, 2006. (Gzipped PostScript, 4 pages, 38244 bytes). (PDF, 181744 bytes).

[53]
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. (Gzipped PostScript, 11 pages, 97656 bytes). Also available as FSP-report S092-6, Austria, 2006, at http://www.ig.jku.at/cgi-bin/CGI/Reports.pl.

[54]
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. (Gzipped PostScript, 11 pages, 112494 bytes). Also available as FSP-report S092-7, Austria, 2006, at http://www.ig.jku.at/cgi-bin/CGI/Reports.pl.

[55]
O. Aichholzer and H. Krasser. Abstract order type extension and new results on the rectilinear crossing number. In Proc. 21th European Workshop on Computational Geometry EWCG '05, pages 61-64, Eindhoven, The Nederlands, 2005. (Gzipped PostScript, 4 pages, 56689 bytes). (PDF, 203417 bytes).

[56]
O. Aichholzer and H. Krasser. Abstract order type extension and new results on the rectilinear crossing number. In Proc. 21th Ann. ACM Symp. Computational Geometry, pages 91-98, Pisa, Italy, 2005. (Gzipped PostScript, 11 pages, 159667 bytes).

[57]
O. Aichholzer, C. Huemer, S. Renkl, B. Speckmann, and C. D. Tóth. On pseudo-convex decompositions, partitions, and coverings. In Proc. 21th European Workshop on Computational Geometry EWCG '05, pages 89-92, Eindhoven, The Nederlands, 2005. (Gzipped PostScript, 4 pages, 170312 bytes). (PDF, 226776 bytes). Also available as FSP-report S092-3, Austria, 2005, at http://www.ig.jku.at/cgi-bin/CGI/Reports.pl.

[58]
O. Aichholzer, T. Hackl, C. Huemer, F. Hurtado, H. Krasser, and B. Vogtenhuber. Bounding the number of plane graphs. In Proc. 15th Annual Fall Workshop on Computational Geometry and Visualization, pages 31-32, Philadelphia, Pennsylvania, USA, 2005.

[59]
O. Aichholzer, D. Bremner, E.D. Demaine, F. Hurtado, E. Kranakis, H. Krasser, S. Ramaswami, S. Sethia, and J. Urrutia. Games on triangulations. Theoretical Computer Science, 343(1-2):42-71, 2005. (PDF, 355952 bytes).

[60]
O. Aichholzer, F. Aurenhammer, C. Huemer, and H. Krasser. Transforming spanning trees and pseudo-triangulations. In Proc. 21th European Workshop on Computational Geometry EWCG '05, pages 81-84, Eindhoven, The Nederlands, 2005. (Gzipped PostScript, 4 pages, 38244 bytes). (PDF, 181744 bytes). Also available as FSP-report S092-10, Austria, 2006, at http://www.ig.jku.at/cgi-bin/CGI/Reports.pl.

[61]
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 Annual Canadian Conference on Computational Geometry CCCG 2005, pages 123-126, Windsor, Ontario, Canada, 2005. (Gzipped PostScript, 4 pages, 56205 bytes). Also available as FSP-report S092-4, Austria, 2005, at http://www.ig.jku.at/cgi-bin/CGI/Reports.pl.

[62]
O. Aichholzer and K. Reinhardt. A quadratic distance bound on sliding between crossing-free spanning trees - extended abstract. In Proc. 20th European Workshop on Computational Geometry EWCG '04, pages 13-16, Sevilla, Spain, 2004. (Gzipped PostScript, 4 pages, 149399 bytes).

[63]
O. Aichholzer, D. Orden, F. Santos, and B. Speckmann. On the number of pseudo-triangulations of certain point sets. In Proc. 20th European Workshop on Computational Geometry EWCG '04, pages 119-122, Sevilla, Spain, 2004. (Gzipped PostScript, 4 pages, 188022 bytes).

[64]
O. Aichholzer, F. Hurtado, and M. Noy. A lower bound on the number of triangulations of planar point sets. Computational Geometry: Theory and Applications, 29(2):135-145, 2004. (Gzipped PostScript, 11 pages, 82635 bytes). (PDF, 146625 bytes). See also the Counting Triangulations - Olympics.

[65]
O. Aichholzer, C. Huemer, and H. Krasser. Triangulations without pointed spanning trees - extended abstract. In Proc. 20th European Workshop on Computational Geometry EWCG '04, pages 221-224, Sevilla, Spain, 2004. (Gzipped PostScript, 4 pages, 131642 bytes).

[66]
O. Aichholzer, F. Aurenhammer, H. Krasser, and B. Speckmann. Convexity minimizes pseudo-triangulations. Computational Geometry: Theory and Applications, 28(1):3-10, 2004. (Gzipped PostScript, 8 pages, 76729 bytes).

[67]
O. Aichholzer, F. Aurenhammer, and B. Palop. Quickest paths, straight skeletons, and the city Voronoi diagram. Discrete & Computational Geometry, 31(1):17-35, 2004. (Gzipped PostScript, 20 pages, 155843 bytes).

[68]
O. Aichholzer, G. Rote, B. Speckmann, and I. Streinu. The zigzag path of a pseudo-triangulation. In Lecture Notes in Computer Science, Proc. 8th International Workshop on Algorithms and Data Structures (WADS), volume 2748, pages 377-389, 2003. (Gzipped PostScript, 12 pages, 193469 bytes).

[69]
O. Aichholzer, D. Orden, F. Santos, and B. Speckmann. On the number of pseudo-triangulations of certain point sets. In Proc. 15th Annual Canadian Conference on Computational Geometry CCCG 2003, pages 141-144, Halifax, Nova Scotia, Canada, 2003. (Gzipped PostScript, 4 pages, 90649 bytes).

[70]
O. Aichholzer, M. Hoffmann, B. Speckmann, and C. D. Tóth. Degree bounds for constrained pseudo-triangulations. In Proc. 15th Annual Canadian Conference on Computational Geometry CCCG 2003, pages 155-158, Halifax, Nova Scotia, Canada, 2003. (Gzipped PostScript, 4 pages, 192920 bytes).

[71]
O. Aichholzer, D. Bremner, E.D. Demaine, F. Hurtado, E. Kranakis, H. Krasser, S. Ramaswami, S. Sethia, and J. Urrutia. Geometric games on triangulations. In Proc. 19th European Workshop on Computational Geometry CG '03 Bonn, pages 89-92, Bonn, Germany, 2003. (Gzipped PostScript, 4 pages, 111150 bytes).

[72]
O. Aichholzer, D. Bremner, E.D. Demaine, F. Hurtado, E. Kranakis, H. Krasser, S. Ramaswami, S. Sethia, and J. Urrutia. Playing with triangulations. In Lecture Notes in Computer Science 2866, Japanese Conference, JCDCG 2002, pages 22-37, 2003. (Gzipped PostScript, 17 pages, 1145218 bytes).

[73]
O. Aichholzer, D. Bremner, E.D. Demaine, D. Meijer, V. Sacristán, and M. Soss. Long proteins with unique optimal foldings in the h-p model. Computational Geometry: Theory and Applications, 25:139-159, 2003. (Gzipped PostScript, 24 pages, 114229 bytes).

[74]
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. (Gzipped PostScript, 33 pages, 147278 bytes).

[75]
O. Aichholzer, F. Aurenhammer, P. Brass, and H. Krasser. Spatial embedding of pseudo-triangulations. In Proc. 19th Ann. ACM Symp. Computational Geometry, volume 19, pages 144-153, San Diego, California, USA, 2003. (Gzipped PostScript, 10 pages, 96092 bytes).

[76]
O. Aichholzer, F. Aurenhammer, F. Hurtado, and H. Krasser. Towards compatible triangulations. Theoretical Computer Science, 296:3-13, 2003. Special Issue. (Gzipped PostScript, 13 pages, 94881 bytes).

[77]
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. (Gzipped PostScript, 12 pages, 125074 bytes).

[78]
O. Aichholzer, B. Speckmann, and I. Streinu. The path of a pseudo-triangulation. In Abstracts of the DIMACS Workshop on Computational Geometry 2002, page 2, Piscataway (NJ), USA, 2002. (PostScript, 132211 bytes).

[79]
O. Aichholzer, C. Cortés, E.D. Demaine, V. Dujmovic, J. Erickson, H. Meijer, M. Overmars, B. Palop, S. Ramaswami, and G.T. Toussaint. Flipturning polygons. Discrete & Computational Geometry, 28(2):231-253, 2002. [Report UU-CS-2000-31, Universiteit Utrecht, The Netherlands, 2000]. (Gzipped PostScript, 26 pages, 140213 bytes). See also Jeff'shomepage about this paper.

[80]
O. Aichholzer, D. Bremner, E.D. Demaine, F. Hurtado, E. Kranakis, H. Krasser, S. Ramaswami, S. Sethia, and J. Urrutia. Playing with triangulations. In Proc. Japan Conference on Discrete and Computational Geometry JCDCG 2002, pages 46-54, Tokyo, Japan, 2002. (Gzipped PostScript, 17 pages, 1145217 bytes).

[81]
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 pages, 117753 bytes). You can also download the nice program MST-Tool we used to check and visualize some of the presented results!

[82]
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. (Gzipped PostScript, 6 pages, 121333 bytes). See also our crossing number homepage.

[83]
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 Warszawa, pages 90-92, Warszawa, Poland, 2002. (Gzipped PostScript, 3 pages, 40990 bytes). See also our crossing number homepage.

[84]
O. Aichholzer, F. Aurenhammer, and H. Krasser. Enumerating order types for small point sets with applications. Order, 19:265-281, 2002. (Gzipped PostScript, 8 pages, 70002 bytes). See also our order type homepage.

[85]
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 pages, 74840 bytes).

[86]
O. Aichholzer, F. Aurenhammer, and H. Krasser. Progress on rectilinear crossing numbers. Technical report, IGI-TU Graz, Austria, 2002. (Gzipped PostScript, 8 pages, 66404 bytes). See also our crossing number homepage.

[87]
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. (Gzipped PostScript, 4 pages, 135036 bytes).

[88]
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. (Gzipped PostScript, 9 pages, 87983 bytes).

[89]
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 pages, 420859 bytes).

[90]
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 pages, 189927 bytes).

[91]
O. Aichholzer, L.S. Alboul, and F. Hurtado. On flips in polyhedral surfaces. International Journal of Foundations of Computer Science (IJFCS), special issue on Volume and Surface Triangulations, 13(2):303-311, 2002. (Gzipped PostScript, 9 pages, 69398 bytes).

[92]
O. Aichholzer and H. Krasser. The point set order type data base: A collection of applications and results. In Proc. 13th Annual Canadian Conference on Computational Geometry CCCG 2001, pages 17-20, Waterloo, Ontario, Canada, 2001. (Gzipped PostScript, 10 pages, 91739 bytes). See also our order type homepage.

[93]
O. Aichholzer, F. Hurtado, and M. Noy. On the number of triangulations every planar point set must have. In Proc. 13th Annual Canadian Conference on Computational Geometry CCCG 2001, pages 13-16, Waterloo, Ontario, Canada, 2001. (Gzipped PostScript, 9 pages, 68831 bytes). See also the Counting Triangulations - Olympics.

[94]
O. Aichholzer, E.D. Demaine, J. Erickson, F. Hurtado, M. Overmars, M.A. Soss, and G.T. Toussaint. Reconfiguring convex polygons. Computational Geometry: Theory and Applications, 20:85-95, 2001. [Report UU-CS-2000-30, Universiteit Utrecht, The Netherlands, 2000]. (Gzipped PostScript, 13 pages, 96869 bytes). (PDF, 141461 bytes).

[95]
O. Aichholzer, D. Bremner, E.D. Demaine, D. Meijer, V. Sacristán, and M. Soss. Long proteins with unique optimal foldings in the h-p model. In Proc. 17th European Workshop on Computational Geometry CG '2001, pages 59-62, Berlin, Germany, 2001. (Gzipped PostScript, 4 pages, 67359 bytes).

[96]
O. Aichholzer, F. Aurenhammer, B. Brandtstätter, H. Krasser, C. Magele, M. Mühlmann, and W. Renhart. Evolution strategy and hierarchical clustering. In 13th COMPUMAG Conference on the Computation of Electromagnetic Fields, Lyon-Evian, France, 2001. (Gzipped PostScript, 2 pages, 253639 bytes).

[97]
O. Aichholzer, F. Aurenhammer, F. Hurtado, and H. Krasser. Towards compatible triangulations. In Jie Wang, editor, Proc. 7th Ann. Int'l. Computing and Combinatorics Conf. COCOON'01, Lecture Notes in Computer Science, volume 2108, pages 101-110, Guilin, China, 2001. Springer Verlag. (Gzipped PostScript, 10 pages, 75423 bytes).

[98]
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 pages, 193642 bytes). (PDF, 385575 bytes).

[99]
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 pages, 42822 bytes).

[100]
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 pages, 70002 bytes). See also our order type homepage.

[101]
O. Aichholzer, L.S. Alboul, and F. Hurtado. On flips in polyhedral surfaces. In Proc. 17th European Workshop on Computational Geometry CG '2001, pages 27-30, Berlin, Germany, 2001. (Gzipped PostScript, 4 pages, 56670 bytes). See also our interactive web-page.

[102]
O. Aichholzer, E.D. Demaine, J. Erickson, F. Hurtado, M. Overmars, M.A. Soss, and G.T. Toussaint. Reconfiguring convex polygons. In Proc. 12th Annual Canadian Conference on Computational Geometry CCCG 2000, pages 17-20, Fredericton, New Brunswick, Canada, 2000. (Gzipped PostScript, 4 pages, 59180 bytes).

[103]
O. Aichholzer, C. Cortés, E.D. Demaine, V. Dujmovic, J. Erickson, H. Meijer, M. Overmars, B. Palop, S. Ramaswami, and G.T. Toussaint. Flipturning polygons. In Proc. Japan Conference on Discrete and Computational Geometry JCDCG 2000, Tokay University, Tokyo, Japan, 2000. (Gzipped PostScript, 2 pages, 27174 bytes). See also Jeff'shomepage about this paper.

[104]
O. Aichholzer, F. Aurenhammer, B. Brandtstätter, 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 pages, 334534 bytes).

[105]
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. (Gzipped PostScript, 5 pages, 63105 bytes). You can download our MST-Tool.

[106]
O. Aichholzer. Extremal properties of 0/1-polytopes of dimension 5. In G. Ziegler and G. Kalai, editors, Polytopes - Combinatorics and Computation, pages 111-130. Birkhäuser, 2000. [SFB-Report F003-132, TU Graz, Austria, 1998]. (Gzipped PostScript, 22 pages, 174202 bytes). You can also investigate 0/1-polytopes by e-mail!

[107]
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 pages, 86020 bytes). Click here for Figures and Animations of Skew Voronoi Diagrams

[108]
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 pages, 60331 bytes).

[109]
O. Aichholzer. The path of a triangulation. In Proc. 15th Ann. ACM Symp. Computational Geometry, pages 14-23, Miami Beach, Florida, USA, 1999. (Gzipped PostScript, 10 pages, 75293 bytes). For an implementation see my page on triangulation counting.

[110]
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 pages, 91693 bytes).

[111]
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 pages, 169152 bytes).

[112]
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, 1998. [SFB-Report F003-050, TU Graz, Austria, 1995]. (Gzipped PostScript, 9 pages, 90570 bytes).

[113]
O. Aichholzer and F. Aurenhammer. Straight skeletons for general polygonal figures in the plane. In A.M. Samoilenko, editor, Voronoi's Impact on Modern Sciences II, volume 21, pages 7-21. Proc. Institute of Mathematics of the National Academy of Sciences of Ukraine, Kiev, Ukraine, 1998. (Gzipped PostScript, 14 pages, 92570 bytes).

[114]
O. Aichholzer. Efficient {0,1}-string searching based on pre-clustering. In Proc. 14th European Workshop on Computational Geometry CG '98, pages 11-13, Barcelona, Spain, 1998. [SFB Report F003-94, TU Graz, Austria, 1996]. (Gzipped PostScript, 21 pages, 157841 bytes).

[115]
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, Würzburg, Germany, 1997. (Gzipped PostScript, 3 pages, 69425 bytes).

[116]
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 pages, 52751 bytes).

[117]
O. Aichholzer, H. Alt, and G. Rote. Matching shapes with a reference point. Int'l Journal of Computational Geometry & Applications, 7(4):349-363, 1997. (Gzipped PostScript, 15 pages, 58931 bytes).

[118]
O. Aichholzer. Combinatorial & Computational Properties of the Hypercube - New Results on Covering, Slicing, Clustering and Searching on the Hypercube. PhD thesis, IGI-TU Graz, Austria, 1997. (Gzipped PostScript, 170 pages, 571907 bytes).

[119]
O. Aichholzer. The path of a triangulation. In Proc. 13th European Workshop on Computational Geometry CG '97, pages 1-3, Würzburg, Germany, 1997. (Gzipped PostScript, 3 pages, 44898 bytes). For an implementation see my page on triangulation counting.

[120]
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 pages, 116106 bytes).

[121]
O. Aichholzer, F. Aurenhammer, G. Rote, and Y.-F. Xu. Constant-level greedy triangulations approximate the MWT well. In Cheng Du, Zhang, editor, Proc. 2nd Int'l. Symp. Operations Research & Applications ISORA'96, Lecture Notes in Operations Research, volume 2, pages 309-318, Guilin, P. R. China, 1996. World Publishing Corporation. (Gzipped PostScript, 10 pages, 60813 bytes).

[122]
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, Münster, Germany, 1996. (Gzipped PostScript, 4 pages, 55367 bytes).

[123]
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 pages, 73640 bytes).

[124]
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 pages, 57810 bytes).

[125]
O. Aichholzer. Clustering the hypercube. SFB-Report F003-93, SFB 'Optimierung und Kontrolle', TU Graz, Austria, 1996. (Gzipped PostScript, 47 pages, 209938 bytes).

[126]
O. Aichholzer, R.L.S. Drysdale, and G. Rote. A simple linear time greedy triangulation algorithm for uniformly distributed points. IIG-Report-Series 408, TU Graz, Austria, 1995. Presented at the Workshop on Computational Geometry, Army MSI Cornell, Stony Brook, 1994. (Gzipped PostScript, 16 pages, 78431 bytes).

[127]
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 pages, 59980 bytes).

[128]
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 pages, 87682 bytes).

[129]
O. Aichholzer, D. Alberts, F. Aurenhammer, and B. Gärtner. 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 pages, 63005 bytes). Click here for the Online Version

[130]
O. Aichholzer, D. Alberts, F. Aurenhammer, and B. Gärtner. Straight skeletons of simple polygons. In Proc. 4th Int. Symp. of LIESMARS, pages 114-124, Wuhan, P. R. China, 1995. (Gzipped PostScript, 11 pages, 49601 bytes).

[131]
O. Aichholzer. Local properties of triangulations. In Proc. 11th European Workshop on Computational Geometry CG '95, pages 27-30, Hagenberg/Linz, Austria, 1995. (Gzipped PostScript, 4 pages, 34089 bytes).

[132]
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 pages, 43528 bytes).

[133]
O. Aichholzer, H. Alt, and G. Rote. Matching shapes with a reference point. In Proc. 10th Ann. ACM Symp. Computational Geometry, pages 85-92, Stony Brook, New York, USA, 1994. (Gzipped PostScript, 8 pages, 61535 bytes).

[134]
O. Aichholzer, H. Alt, and G. Rote. Matching shapes with a reference point. In Proc. 10th European Workshop on Computational Geometry CG '94, pages 81-84, Santander, Spain, 1994. (Gzipped PostScript, 8 pages, 61535 bytes).

[135]
O. Aichholzer and H. Hassler. A fast method for modulus reduction in residue number system. In Proc. epp'93, pages 41-54, Vienna, Austria, 1993. [IIG-Report-Series 312, TU Graz, Austria, 1991]. (Gzipped PostScript, 11 pages, 77495 bytes).

[136]
O. Aichholzer. Hyperebenen in Hyperkuben - Eine Klassifizierung und Quantifizierung. Master's thesis, IGI-TU Graz, Austria, 1992. (Gzipped PostScript, 117 pages, 336546 bytes).

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