Peter Brass Publications

State as of 10 September 2007

  1. P. Brass, I. Mengersen: Construction of special edge-colorings, Utilitas Mathematica 36 (1989) 201-210
  2. P. Brass: The maximum number of second smallest distances in a finite planar set, Discrete & Computational Geometry 7 (1992) 371-379
  3. P. Brass: On the maximum densities of j-th smallest distances, Coll. Math. Soc. Janos Bolyai 60 119-126 Tagungsband zu `Sets, Graphs and Numbers' 1991
  4. P. Brass: Beweis einer Vermutung von Erdös und Pach aus der kombinatorischen Geometrie, Dissertation, TU Braunschweig 1992
  5. P. Brass: Triangulations and Lattice Points, Beiträge zur Algebra und Geometrie 34 (1993) 9-14
  6. K. Bezdek, P. Brass, H. Harborth: Maximum Convex Hulls of Connected Systems of Segments and of Polyominoes, Beiträge zur Algebra und Geometrie 35 (1994) 37-43
  7. P. Brass, H. Harborth, H. Nienborg: On the maximum size of a C_4-free subgraph of Q_n, Journal of Graph Theory 19 (1995) 17-23
  8. P. Brass: Packing constants in graphs and connectivity, Discrete Mathematics 137 (1995) 353-355
  9. P. Brass: Symmetric Chain Partitions of Orthocomplemented Posets, International Journal of Theoretical Physics 34 (1995) 1241-1245.
  10. P. Brass: On the Erdös-diameter of sets, Discrete Mathematics 150 (1996) 415-419.
  11. P. Brass: Erdös Distance Problems in Normed Spaces, Computational Geometry - Theory and Applications 6 (1996) 195-214.
  12. P. Brass: On the Quantitative Steinitz Theorem in the Plane, Discrete & Computational Geometry 17 (1997) 111-117.
  13. P. Brass, I. Herburt : On point sets fixing a convex body from within, Beiträge zur Algebra und Geometrie 38 (1997) 87-90.
  14. P. Brass: On the maximum number of unit distances among n points in dimension four, Bolyai Soc. Mathematical Studies 4 (1997) 277-290.
  15. P. Brass: Häufige Abstände in endlichen Punktmengen, Jahrbuch Überblicke Mathematik 1998, 66-75.
  16. P. Brass: On point sets with many unit distances in few directions, Discrete & Computational Geometry 19 (1998) 355-366.
  17. P. Brass: On convex lattice polyhedra and pseudocircle arrangements, in: `Charlemagne and his Heritage - 1200 Years of Civilization an Science in Europe. Vol 2: Mathematical Arts' (P.L. Butzer, H.Th. Jongen, W. Oberschelp, Eds.) Brepols Verlag 1998, 297-302
  18. P. Brass: On the diameter of sets with maximum number of unit distances, Geombinatorics 8 (1998) 149-153
  19. P. Brass: Extremal orthoposets without forbidden substructures, International Journal of Theoretical Physics 37 (1998) 3-9
  20. P. Brass: Isoperimetric inequalities for lattice-periodic sets, Monatshefte fuer Mathematik 127 (1999) 177-181
  21. P. Brass: Equilateral Simplices in normed spaces, Beiträge zur Algebra und Geometrie 40 (1999) 303-307
  22. P. Brass: On strongly normal tesselations, Pattern recognition letters 20 (1999) 957-960
  23. P. Brass: Geometrie in der Mustererkennung, in: `Mathematik - Interdisziplinär' (J. Flachsmeyer, R. Fritsch, H.-C. Reichel, Eds.) Shaker-Verlag, Aachen, 2000, 67-75
  24. P. Brass, C. Knauer: Testing the congruence of d-dimensional pointsets, 'SCG 2000' (16th Annual ACM Symp. Comput. Geom.) ACM-Press 2000, 310-314 also in International Journal on Computational Geometry 12 (2002) 115-124
  25. P. Brass, C. Wenk: On the number of cylinders touching a ball', Geometriae Dedicata 81 (2000) 281-284
  26. P. Brass: Exact point pattern matching and the number of congruent triangles in a threedimensional point set, `ESA 2000' (European Symposium on Algorithms) Springer LNCS 1879 112-119
  27. P. Brass, M. Lassak: Problems on approximation by triangles, Geombinatorics 10 (2001) 103-115
  28. P. Brass, J. Pach: The maximum number of times the same distance can occur among the vertices of a convex $n$-gon is O(n log n), J. Combinatorial Theory Ser. A 94 (2001) 178-179
  29. P. Brass, G. Rote, K. Swanepoel: Triangles of extremal area or perimeter in a finite planar pointset, Discrete & Computational Geometry 26 (2001) 51-58
  30. P. Brass: On finding maximum-cardinality symmetric subsets, `JCDCG 2000' (Japanese Conf. Disc. Comput. Geom.) (J. Akiyama, M. Kano, M. Urabe, Eds.) Springer LNCS 2098 (2001) 106-112 also Computational Geometry - Theory and Applications) 24 (2003) 19-25
  31. P. Brass: On the nonexistence of Hausdorff-like distance measures for fuzzy sets, Pattern Recognition Letters 23 (2002) 39-43.
  32. P. Brass: Combinatorial geometry problems in pattern recognition, Discrete & Computational Geometry 28 (2002) 495-510.
  33. P. Brass: On point sets with no k collinear points, `Discrete Geometry: In honor of W. Kuperberg's 60th birthday' (A. Bezdek, ed.) Marcel Dekker Inc., Pure and Applied Math. Ser. Vol. 253, 2003, 185-192.
  34. P. Brass, C. Knauer: On counting point-hyperplane incidences, Computational Geometry - Theory and Applications 25 (2003) 13-20.
  35. P. Brass, E. Cenek, C.A. Duncan, A. Efrat, C. Erten, D. Imailescu, S.G. Kobourov, A. Lubiw, J.S.B. Mitchell: On simultaneous planar graph embedding, `WADS 2003' (Workshop Alg. Data Struct.) Springer LNCS 2748 (2003) 243-255.
  36. O. Aichholzer, O. Aurenhammer, H. Krasser, P. Brass: Pseudo-triangulations from surfaces and a novel type of edge-flip, `SCG 2003' (19th Annual ACM Symp Comput. Geom.) ACM-Press 2003, 144-153.
  37. H. Alt, P. Brass, M. Godau, C. Knauer, C. Wenk: Computing the Hausdorff distance of geometric patterns and shapes, in: `Discrete and Computational Geometry - the Goodman-Pollack Festschrift' (B. Aronov et al., eds.) Springer 2003, 65-76.
  38. P. Brass, G. Karolyi, P. Valtr: A Turan-type extremal theory for convex geometric graphs, in: `Discrete and Computational Geometry - the Goodman-Pollack Festschrift' (B. Aronov et al., eds.) Springer 2003, 275-300.
  39. P. Brass, K. Bezdek: On k^+-neighbour packings and one-sided Hadwiger configurations, Beiträge zur Algebra und Geometrie 44 (2003) 493-498.
  40. P. Brass, L. Heinrich-Litan, P. Morin: Computing the center of area of a convex polygon, International Journal on Computational Geometry 13 (2003) 439-445.
  41. O. Aichholzer, O. Aurenhammer, H. Krasser, P. Brass: Pseudo-triangulations from surfaces and a novel type of edge-flip, SIAM Journal on Computing 32 (2003) 1621-1653.
  42. P. Brass, C. Knauer: Testing congruence and symmetries for general 3-dimensional objects, Computational Geometry - Theory and Applications 27 (2004) 3-11.
  43. P. Brass: Turan-type extremal problems for convex geometric hypergraphs, in `Towards a theory of geometric graphs' (J. Pach, ed.), Contemporary Mathematics 342, AMS 2004, 25-33.
  44. P. Brass: Empty monochromatic fourgons in two-colored point sets, Geombinatorics 14 (2004) 5-7.
  45. T. Asano, P. Brass, S. Sasahara: Disc covering problem, with application to digital halftoning, `ICCSA 2004 - CGA04' (Workshop Comput. Geom. Appl., as part of Int. Conf. Computat. Sci. Appl.) Proc. Part III, Springer LNCS 3045 (2004) 11-21.
  46. H.-K. Ahn, P. Brass, O. Cheong, H.-S. Na, C.-S. Shin, A.Vigneron: Approximation algorithms for inscribing or circumscribing an axially symmetric polygon to a convex polygon, `COCOON 2004' (Comput. Combin. Conf.) Springer LNCS 3106 (2004) 259-267.
  47. P. Brass: An upper bound for the d-dimensional analogue of Heilbronn's triangle problem, SIAM Journal of Discrete Mathematics 19 (2005) 192--195.
  48. P. Brass: On the size of higher-dimensional triangulations, in: Current Trends in Combinatorial and Computational Geometry --- Papers from the Special Program at MSRI, J.E. Goodman et al., Eds.., MSRI Publications 52 (2005) Cambridge Univ. Press 147--153.
  49. P. Brass, J. Pach: Problems and results on geometric patterns, in: Graph Theory and Combinatorial Optimization}, D. Avis et al., Eds., Kluwer Academic Publishers 2005, 17--36.
  50. B. Liu, P. Brass, O. Dousse, P. Nain, D. Towsley: Mobility improves coverage in sensor networks, in: MobiHoc 2005 (Proc. ACM Conference on Mobile Ad-Hoc Networks and Computing) 300--308.
  51. P. Brass, W. Moser, J. Pach: Research Problems in Discrete Geometry, Springer-Verlag 2005, 506pp., ISBN 0-387-23815-8, $69.95.
  52. P. Brass, M. Sharifi: A lower bound for Lebesgue's universal cover problem, International Journal on Computational Geometry & Applications 15 (2005) 537--544.
  53. H.-K. Ahn, P. Brass, O. Cheong, H.-S. Na, C.-S. Shin, A. Vigneron: Inscribing an axially symmetric polygon and other approximation algorithms for planar convex sets, Computational Geometry - Theory and Applications 33 (2006) 152--164.
  54. P. Brass, E. Cenek, C.A. Duncan, A. Efrat, C. Erten, D. Imailescu, S.G. Kobourov, A. Lubiw, J.S.B. Mitchell: On simultaneous planar graph embedding, Computational Geometry - Theory and Applications 36 (2007) 117--130.
  55. P. Brass: Multidimensional heaps and complementary range searching, Information Processing Letters 102 (2007) 152--155.
  56. P. Brass: Bounds on coverage capabilities for models of networks of mobile sensors, ACM Transactions on Sensor Networks 3(2) 2007, Article 9.
  57. H.-K. Ahn, H. Alt, T. Asano, S.W. Bae,P. Brass, O. Cheong, C. Knauer, H.-S. Na, C.-S. Shin, A. Wolff: Constructing Optimal Highways, in: CATS 2007 (Computing: The Australasian Theory Symposium) Australian Computer Societ CRPIT Series Vol 65, J. Gudmundsson, B. Jay, eds.
  58. P. Brass, K.D. Kim, H.-S. Na, C.-S. Shin: Escaping Offline Searchers and a Discrete Isoperimetric Theorem, in: ISAAC 2007 (Proc 18th International Symposium on Algorithms and Computation), Springer LNCS 4835 (2007) 65--74
  59. H.-K. Ahn, P. Bra\ss, C.-S. Shin: Maximum Overlap and Minimum Convex Hull of Two Convex Polyhedra under Translations}, Computational Geometry --- Theory and Applications 40 (2008) 171--177.