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Publications, subproject 05BiBTeX



    Journal articles

  1. 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 to appear (2010).
  2. 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 accepted (2010).
  3. O. Aichholzer, S. Cabello, R. Fabila-Monroy, D. Flores-Peñaloza, T. Hackl, C. Huemer, F. Hurtado, and D. Wood. Edge-removal and non-crossing configurations in geometric graphs. Discrete Mathematics & Theoretical Computer Science (DMTCS) accepted (2010).
  4. 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) 23/4 (2010), 2147-2155. [doi].
  5. F. Aurenhammer and B. Jüttler. On computing the convex hull of (piecewise) spherical objects. submitted to journal (2010).
  6. E. Ackerman, O. Aichholzer, and B. Keszegh. Improved upper bounds on the reflexivity of point sets. Computational Geometry: Theory and Applications 42 (2009), 241-249.
  7. 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 (2009), 339-349, Special issue: Voronoi Diagrams and their Applications. [doi].
  8. O. Aichholzer, F. Aurenhammer, T. Hackl, and B. Speckmann. On minimum weight pseudo-triangulations. Computational Geometry: Theory and Applications 42/6-7 (2009), 627-631.
  9. O. Aichholzer, S. Bereg, A. Dumitrescu, A. Garc'ia, 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 (2009), 617-626.
  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 (2009), 934-938. [doi].
  11. O. Aichholzer, J. Garc'ia, D. Orden, and P. Ramos. New results on lower bounds for the number of~(leq k)-facets. European Journal of Combinatorics 30 (2009), 1568-1574.
  12. 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) (2008), 134-141.
  13. 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 (2008), 201-206.
  14. O. Aichholzer, C. Huemer, and H. Krasser. Triangulations without pointed spanning trees. Computational Geometry: Theory and Applications 40 (2008), 79-83.
  15. 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) (2008), 254-278.
  16. O. Aichholzer, F. Aurenhammer, and T. Hackl. Pre-triangulations and liftable complexes. Discrete & Computational Geometry 38 (2007), 701-725.
  17. O. Aichholzer, F. Aurenhammer, T. Hackl, and C. Huemer. Connecting colored point sets. Discrete Applied Mathematics 155/3 (2007), 271-278.
  18. O. Aichholzer, F. Aurenhammer, C. Huemer, and B. Vogtenhuber. Gray code enumeration of plane straight-line graphs. Graphs and Combinatorics (Springer) 23(5) (2007), 467-479.
  19. O. Aichholzer, J. García, D. Orden, and P. Ramos. New lower bounds for the number of (leq k)-edges and the rectilinear crossing number of k_n. Discrete & Computational Geometry 38 (2007), 1-14.
  20. 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) (2007), 67-84.
  21. 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) (2007), 481-507.
  22. O. Aichholzer and K. Reinhardt. A quadratic distance bound on sliding between crossing-free spanning trees. Computational Geometry: Theory and Applications, special issue 37 (2007), 155-161.
  23. F. Aurenhammer. Weighted skeletons and fixed-share decomposition. Computational Geometry: Theory and Applications 40 (2007), 93-101.
  24. F. Aurenhammer and Y.-F.Xu. Optimal triangulations. In P. C.A.Floudas, editor, Encyclopedia of Optimization, Second Edition. Kluwer Academic Publishing, 2007.
  25. O. Aichholzer, F. Aurenhammer, C. Huemer, and H. Krasser. Transforming spanning trees and pseudo-triangulations. Information Processing Letters (IPL) 97(1) (2006), 19-22.
  26. O. Aichholzer, F. Aurenhammer, and H. Krasser. On the crossing number of complete graphs. Computing 76 (2006), 165-176.
  27. 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 (2006), 2-15.
  28. F. Aurenhammer, R.L.S.Drysdale, and H. Krasser. Farthest line segment Voronoi diagrams. Information Processing Letters 100 (2006), 220-225.
  29. F. Aurenhammer and H. Krasser. Pseudo-simplicial complexes from maximal locally convex functions. Discrete & Computional Geometry 35 (2006), 201-221.

    Refereed articles in books and conference proceedings

  30. O. Aichholzer. [Empty] [colored] k-gons - Recent results on some Erdös-Szekeres type problems. In Proc. XIII Encuentros de Geometr'ia Computacional, pages 43-52, Zaragoza, Spain, 2009.
  31. O. Aichholzer, W. Aigner, F. Aurenhammer, T. Hackl, B. Jüttler, E. Pilgerstorfer, and M. Rabl. Divide-and-conquer for voronoi diagrams revisited. In 25^th Ann. ACM Symp. Computational Geometry, pages 189-197, Aarhus, Denmark, 2009.
  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. 25^th European Workshop on Computational Geometry EuroCG '09, pages 293-296, Brussels, Belgium, 2009.
  33. 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. 25^th European Workshop on Computational Geometry EuroCG '09, pages 139-142, Brussels, Belgium, 2009.
  34. O. Aichholzer, F. Aurenhammer, F. Hurtado, P. Ramos, and J. Urrutia. Two-convex polygons. In Proc. 25^th European Workshop on Computational Geometry EuroCG '09, pages 117-120, Brussels, Belgium, 2009.
  35. 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.
  36. O. Aichholzer, R. Fabila-Monroy, D. Flores-Peñaloza, T. Hackl, C. Huemer, J. Urrutia, and B. Vogtenhuber. Modem illumination of monotone polygons. In Proc. 25^th European Workshop on Computational Geometry EuroCG '09, pages 167-170, Brussels, Belgium, 2009.
  37. 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.
  38. O. Aichholzer, T. Hackl, C. Huemer, F. Hurtado, and B. Vogtenhuber. Large bichromatic point sets admit empty monochromatic 4-gons. In Proc. 25^th European Workshop on Computational Geometry EuroCG '09, pages 133-136, Brussels, Belgium, 2009.
  39. 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.
  40. O. Aichholzer, F. Aurenhammer, T. Hackl, B. Kornberger, S. Plantinga, G. Rote, A. Sturm, and G. Vegter. Seed polytopes for incremental approximation. In Proc. 24^th European Workshop on Computational Geometry EuroCG '08, pages 13-16, Nancy, France, 2008.
  41. 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.
  42. O. Aichholzer, S. Cabello, R. Fabila-Monroy, D. Flores-Peñaloza, T. Hackl, C. Huemer, F. Hurtado, and D. Wood. Edge-removal and non-crossing configurations in geometric graphs. In Proc. 24^th European Workshop on Computational Geometry EuroCG '08, pages 119-122, Nancy, France, 2008.
  43. 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.
  44. 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.
  45. 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.
  46. O. Aichholzer, F. Aurenhammer, T. Hackl, B. Kornberger, M. Peternell, and H. Pottmann. Approximating boundary-triangulated objects with balls. In Proc. 23^rd European Workshop on Computational Geometry EuroCG '07, pages 130-133, Graz, Austria, 2007.
  47. 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.
  48. O. Aichholzer, J. García, D. Orden, and P. 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.
  49. 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.
  50. 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. 23^rd European Workshop on Computational Geometry EuroCG '07, pages 98-101, Graz, Austria, 2007.
  51. 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.
  52. F. Aurenhammer, J. Wallner, M. Peternell, and H. Pottmann. Voronoi diagrams for oriented spheres. In C. Gold, editor, Proc. ISVD'07: 4th Int. Conf. Voronoi Diagrams in Science and Engineering, pages 33-37. IEEE Computer Society, 2007, ISBN 0-7695-2869-4. [doi].
  53. O. Aichholzer, F. Aurenhammer, and T. Hackl. Pre-triangulations and liftable complexes. In 22^nd Ann. ACM Symp. Computational Geometry, pages 282-291, Sedona, Arizona, USA, 2006.
  54. O. Aichholzer, F. Aurenhammer, C. Huemer, and B. Vogtenhuber. Gray code enumeration of plane straight-line graphs. In Proc. 22^nd European Workshop on Computational Geometry EuroCG '06, pages 71-74, Delphi, Greece, 2006.
  55. 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.
  56. O. Aichholzer, C. Huemer, S. Renkl, B. Speckmann, and C. D. Tóth. Decompositions, partitions, and coverings with convex polygons and pseudo-triangles. In P. U. Rastislav Královic, editor, Proceedings 31^st International Symposium on Mathematical Foundations of Computer Science, Lecture Notes in Computer Science, volume 4162, pages 86-97, Stará Lesná, Slovakia, 2006.
  57. O. Aichholzer, D. Orden, and P. Ramos. On the structure of sets attaining the rectilinear crossing number. In Proc. 22^nd European Workshop on Computational Geometry EuroCG '06, pages 43-46, Delphi, Greece, 2006.
  58. 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.
  59. 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.
  60. O. Aichholzer and H. Krasser. Abstract order type extension and new results on the rectilinear crossing number. In Proc. 21^th Ann. ACM Symp. Computational Geometry, pages 91-98, Pisa, Italy, 2005.
  61. B. Aronov, F. Aurenhammer, F. Hurtado, S. Langerman, D. Rappaport, S. Smorodinsky, and C. Seara. Small weak epsilon nets. In Proc. 17^th Canadian Conference on Computational Geometry CCCG '05, pages 51-54, Windsor, Ontario, 2005.



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