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Computational geometry: a retrospective

Published:23 May 1994Publication History
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References

  1. 1.Agarwal, P.K. Partitioning arrangements of lines 11: Applications, Disc. Comput. Geom., 5 (1990), 533-573.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. 2.Agarwal, P.K. Ray shooting and other applications o/ spanning trees with low stabbing number, SIAM J. Cornput., 22 (1992), 540-570.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. 3.Agarwal, P.K., Aronov, B. Counting facets and incidences, Disc. Comput. Geom., 7 (1992), 359-369.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. 4.Agarwal, P.K., Matou#ek, J. Ray shooting and parametric search, SIAM J. Comput., 22 (1993), 794-806.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. 5.Agarwal, P.K., Matou#ek, J. Range searching with semialgebraic sets, Disc. Comput. Geom. (1994), in press.]]Google ScholarGoogle Scholar
  6. 6.Agarwal, P.K., Sharir, M. Application of a new space partitioning technique, Disc. Comput. Geom., 9 (1993), 11-38.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. 7.Agarwal, P.K., Sharir, M., Shot, P. Sharp upper and lower bounds on the length of general Davenport- Schinzel sequences, J. Combin. Theory Ser. A, 52 (1989), 228-274.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. 8.Agarwal, P.K., Sharir, M., Toledo, S. Applications of parametric searching in geometric optimization, Proc. 3rd ACM-SIAM Syrup. Disc. Alg. (1992), 72-82.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. 9.Agarwal, P.K., Sharir, M., Toledo, S. An efficient multi-dimensional searching technique and its applications, Tech. Rep. CS-1993-20, Duke University, 1993."]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. 10.Aggarwal, A., Chazelle, B., Guibaz, L.J., O'Dfinlaing, C., Yap, C.K. Parallel computational geometry, Algorithmica, 3 (1988), 293-327.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. 11.Ajtai, M., Megiddo, N. A deterministic Poly(loglog N)-time N-processor algorithm .for linear programming in fixed dimension, Proc. 24th Ann. ACM Syrup. Theory Comput. (1992), 327-338.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. 12.Alon, N., Babai, L., Itai, A. A fast and simple randomized algorithm/or the maximal independent set problem, J. Algorithms, 7 (1986), 567-583.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. 13.Alon, N., B~r~ny, I., Fiiredi, Z., Kleitman, D. Point selections and weak e-nets for convex hulls, Combinatorics, Probability and Computing, 3 (1992), 189-200.]]Google ScholarGoogle ScholarCross RefCross Ref
  14. 14.Alon. N., Coldrelch. O., Hastad, J., Pera}ta, R. Simple constructions of almost k-wise independent random variables, Random Structures & Algorithms, 3 (1992), 289-304.]]Google ScholarGoogle Scholar
  15. 15.Alon, N., Spencer, J.H. The Probabilistic Method, John Wiley & Sons, 1992.]]Google ScholarGoogle Scholar
  16. 16.Arkin, E.M., Chew, L. P., Huttenlocher, D. P., Kedem, K., Mitchell, J.S.B. An efficiently computable metric for comparing polygonal shapes Proc. 1st ACM-SIAM Symp. Disc. Alg. (1990), 129-137.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. 17.Aronov, B., Matou#ek, J., Sharir, M. On the sum of squares of cell complexities in hyperplane arrangements, Proc. 7th Ann. Syrup. Comput. Geom. (1991), 307-313. To appear in J. Combin. Theory Ser. A.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. 18.Aronov, B., Pellegrini, M., Sharir, M. On the zone of a surface in a hyperplane arrangement, Disc. Comput. Geom., 9 (1993), 177-186.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. 19.Aronov, B., Sharir, M. Triangles in space or building (and analyzing) castles in the air, Combinatorica, 10 (1990), 137-173.]]Google ScholarGoogle ScholarCross RefCross Ref
  20. 20.Aronov, B., Sharir, M. Castles in the air revisited, Proc. 8th Ann. ACM Syrup. Comput. Geom. (1992), 146-156. To appear in Disc. Comput. Geom.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. 21.Aronov, B., Sharir, M. The union of convex polyhedra in three dimensions, Proc. 34th Ann. IEEE Symp. Foundat. Comput. Sci. (1993), 518-527.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. 22.Aurenhammer, F. Power diagrams: properties, algorithms and applications, SIAM J. Comput., 16 (1987), 78-96.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. 23.Aurenhamm#r, F. Voronoi diagrams: a survey of a fundamental geometric data structure, ACM Comput. Surv., 23 (1991), 345-405.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. 24.Bajaj, C.L., Dey, T.K. Convex decompositions of poly. hedra and robustness, SIAM J. Comput., 21 (1992), 339-364.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. 25.Basu, S., Pollack, R., Roy, M.-F. On the combinato. rial and algebraic complexity of quantifier elimination, manuscript, 1994.]]Google ScholarGoogle Scholar
  26. 26.Basu, S., Pollack, R., Roy, M.-F. A new algorithm to find a point in every cell defined by a family of polynomials, in "Quantifier Elimination and Cylindrical Algebraic Decomposition", ed. B. Caviness and J. Johnson, Springer-Verlag, to appear.]]Google ScholarGoogle Scholar
  27. 27.Basu, S., Pollack, R., Roy, M.-F. On the number of cells defined by a family of polynomials on a variety, Algorithmic foundations of robotics, AK Peters, ed. K.Y. Goldberg, D. H alperin, J.-C. Latombe, R.H. Wilson. To appear.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. 28.Beck, J. An algorithmic approach to the Lovdsz local lemma. L Random Structures & Algorithms, 2 (1991), 343-365.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. 29.Ben-Or, M. Lower bounds for algebraic computation trees, Proc. 15th Ann. ACM Syrup. Theory Comput. (1983), 80-86.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. 30.Ben-Or, M., Kozen, D., Reif, J. The complexity of elementary algebra and geometry, J. Comput. Syst. Sci., 32 (# 986), 251-264.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. 31.Bentley, J.L., Ottmann, T.A. Algorithms for reporting and counting geometric intersections, IEEE Trans. Comput., C-28 (1979), 643-647.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. 32.Berger, B., Rompel, J. Simulating (logn)~-wise independence in NC, J. ACM, 38 (1991), 1028-1046.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. 33.Berger, B., Rompel, J., Shor, P. Efficient NC algorithms for set cover with applications to learnin9 and geometry, Proc. 30th Ann. IEEE Syrup. Foundat. Cornput. Sci., (1989), 54-59.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. 34.Bern, M. Compatible tetrahedralizations, Proc. 9th Ann. ACM Syrup. Comput. Geom. (1993), 281-288.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  35. 35.Bern, M., Dobkin, D., Eppstein, D. Triangulatm9 polygons without lar9e angles, Proc. 8th Ann. ACM Symp. Comput. Geom. (1992), 222-231.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  36. 36.Bern, M., Eppstein, D. Mesh generation and optimal triangulation, in: Computing in Euclidean Geometry, 1, World Scientific, ed. D. Z. Du and F. K. Hwang (1992), 23-90.]]Google ScholarGoogle Scholar
  37. 37.Bern, M., Eppstein, D., Gilbert, J. Provably 9ood mesh generation, Ptoc. 31st Ann. IEEE Syrup. Foundat. Comput. Sci. (1990), 231-241.]]Google ScholarGoogle Scholar
  38. 38.BjSrner, A., Lov~sz, L., Yao, A.C. Linear decision trees: volume estimates and topological bounds, Proc. 24th Ann. ACM Syrup. Theory Comput. (1992), 17q- 177.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  39. 39.Bochnak, J., Coste, M., Roy. M.-F. Gdomdtrie algdbrique rdelle, Springer Verlag, I-Ieidelberg, 1987.]]Google ScholarGoogle Scholar
  40. 40.Boissonnat, J.D., Devillers, O., Schott, R., Teillaud, M., Yvinec, M. Applications of random sampling to online algorithms in computational geometry, Disc. Cornput. Geom., 8 (1992), 51-71.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  41. 41.Boissonnat, j.D., Teillaud, M. On the randomized construction of the Delaunay tree, Theoret. Comput. Sci., 112 (1993), 339-354.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  42. 42.Br6nnimann, H., Ch#zelle, B., Matou#ek, J. Product range spaces, sensitive sampling, and derandomization, Proc. 34th Ann. IEEE Syrup. Foundat. Comput. Sci. (1993), 400-409.]]Google ScholarGoogle Scholar
  43. 43.BrSnnimann, H., Chazelle, B., Pach, J. How hard is halfspace range searching?# Disc. Comput. Geom.# 10 (1993), 143-155.]]Google ScholarGoogle Scholar
  44. 44.Canny, J. The Complexity of Robot Motion Planning, MIT Press, 1987.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  45. 45.Canny, J. Some algebraic and geometric computations in PSPAGE, Proc. 20th Ann. ACM Syrup. Theory Comput. (1988), 460-467.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  46. 46.Canny, J. Generalized charactemstic polynomials, J. Symbolic Comput., 9 (1990), 241-250.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  47. 47.Canny, J. Some Practical Tools for Algebraic Geometry, Tech. Rep., Spring school on robot motion planning, Promotion Esprit, 1993.]]Google ScholarGoogle Scholar
  48. 48.Canny, J. Computing road maps #n general semialgebraic sets, The Computer Journal, 36 (1993), 504- 514.]]Google ScholarGoogle ScholarCross RefCross Ref
  49. 49.Canny, J. Improved algorithms for sign determination and existential quantifier elimination, The Computer Journal, 36 (1993), 409-418.]]Google ScholarGoogle ScholarCross RefCross Ref
  50. 50.Canny, J., Donald, B.R., Ressler, G. A rational rotation method for robust geometric algorithms, Proc. 8th Ann. ACM Syrup. Comput. Geom. (1992), 251-260.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  51. 51.Chazelle, B. Convex partitions of polyhedra: a lower bound and worst-case optimal algorithra, SIAM J. Cornput., 13 (1984), 488-507.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  52. 52.Chazelle, B. Filtering search: A new approach to queryanswering, SIAM J. Comput., 15 (1986), 703-724.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  53. 53.Chazelle, B. Lower bounds on the complexity of polytope range searching, J. Amer. Math. Soc., 2 (1989), 637- 666.]]Google ScholarGoogle ScholarCross RefCross Ref
  54. 54.Chazelle, B. Lower bounds for orthogonal range searching: I. the reporting case, IL the arithmetic model, J. ACM, 37 (1990), 200-212 and 439-463.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  55. 55.Chazelle, B. Triangulating a simple polygon in linear time, Disc. Comput. Geom., 6 (1991), 485-524.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  56. 56.Chazelle, B. An optimal algorithm for intersecting three-dimensional convex polyhedrc# SIAM J. Comput., 21 (1992), 671-696.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  57. 57.Chazelle, B. Cutting hyperplanes .for divzde-andconquer, Disc. Comput. Geom., 9 (1993), 145-158.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  58. 58.Chazelle, B. An optimal convex hull algorithm in any fixed dimension, Disc. Comput. Geom., 10 (1993), 377- 409.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  59. 59.Chazelle, B., Dobkin, D.P. Optimal convex decompositions, Computational Geometry, G.T. Toussaint, ed., North-Holland (1985), 63-133.]]Google ScholarGoogle Scholar
  60. 60.Chazelle, B., Edelsbrunner, H. An optimal algorithm for intersecting line segments in the plane, J. ACM 39 (1992), 1-54.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  61. 61.Chazelle, B., Edelsbrunner, H. Grigni, M., Guibas, L.J., Hershberger, J., Sharir, M., Snoeyink, J. Ray shooting in polygons using geodesic triangulations, Proc. 18th ICALP, LNCS, Springer-Verlag (1991), 661- 673.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  62. 62.Chazelle, B., Edelsbrunner, H., Grigni, M., Guibas, L.J., Sharir, M., Welzl, E. Improved bounds on weak e-nets for convex sets, Proc. 25th Ann. ACM Syrup. Theory of Comput. (1993).]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  63. 63.Ghazelle, D., Edelsbrunner, H., Guibas, L.J., Sharir, M. Lines in space combinatorics, algorithms and applications, Proc. 21st Ann. ACM Syrup. Theory of Comput. (1989), 382-393.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  64. 64.Chazelle, B., Edelsbrunner, H., Guibas, L.J., Sharir, M. A singly-exponential stratification scheme for real semi-algebraic varieties and its applications, Theoret. Comput. Sci., 84 (1991), 77-105.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  65. 65.Chazelle, B., Edelsbrunner, H., Guibas, L.J., Sharir, M. Diameter, width, closest line pair, and parametric searching, Disc. Comput. Geom., 10 (1993), 183-196.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  66. 66.Chazelle, B., Edelsbrurmer, H., Guibas, L.J., Sharir, M., Snoeyink, J. Computing a face in an arrangement of line segments and related problems, SIAM J. Cornput., 22 (1993), 1286-1302.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  67. 67.Chazelle, B., Friedman, J. A deterministic view of random sampling and its use in geometry, Combinatorica, 10 (1990), 229-249.]]Google ScholarGoogle Scholar
  68. 68.Chazelle, B., Guibas, L.J. Visibility and intersection problems in plane geometry, Disc. Comput. Geom., 4 (1989), 551-581.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  69. 69.Chazelle, B., Guibas, L.J. Fractional cascading: L A data structuring technique, IL Applications, Algorithmic#, 1 (1986), 133-162 and 163-191.]]Google ScholarGoogle Scholar
  70. 70.Chazelle, B., Matou#ek, J. On linear-time deterministic algorithms for optimization problems in fixed dimension, Proc. 4th Ann. ACM-SIAM Symp. Disc. Alg. (1993), 281-290.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  71. 71.Chazelle, B., Matougek, J. Derandomizing an outputsensitive convex hull algorithm in three dimensions, Comput. Geom.: Theory and Appl. (1994), to appear.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  72. 72.Chazelle, B., Palios, L. Triangulating a nonconvex polytope, Disc. Comput. Geom., 5 (1990), 505-526.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  73. 73.Chazelle, B., Rosenberg, B. Lower bounds on the complexity of simplex range reporting on a pointer machine, Proc. t9th ICALP, LNCS 623, Springer-Verlag (1992), 439-449.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  74. 74.Chazelle, B., Sharir, M. An algorithm for generalized point location and its applications, J. Symbolic Cornput., 10 (1990), 281-309.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  75. 75.Ch#zelle, B., Sharir, M., Welzl, E. Quasi-optimal up. per bounds for simplex range searching and new zor#e theorems, Algorithmica, 8 (1992), 407-429.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  76. 76.Chazelle, B., Shouraboura, N. Bounds on the size of tetrahedralizations, Proc. 10th Ann. ACM Symp. Cornput. Geom. (1994), to appear.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  77. 77.Chazelle, B., Welzl, E. Quasi-optimal range searching in spaces of finite VC-dimension, Disc. Comput. Geom., 4 (1989), 467-489.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  78. 78.Cheng, S.W., Janardan, R. New results on dynamic planar point location, SIAM J. Comput., 21 (1992), 972-999.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  79. 79.Chiang, Y.J., Preparata, F.P., Tamassia, R. A unified approach to dynamic point location, ray shooting, and shortest paths in planar maps, Proc. 4th ACM-SIAM Symp. Disc. Alg. (1993), 44-53.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  80. 80.Clarkson, K.L. Linear programming in O(n x 3 ) time, Inf. Process. Lett., 22 (1986), 21-24.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  81. 81.Clarkson, K.L. New applications of random sampling in computational geometry, Disc. Comput. Geom., 2 (1987), 195-222.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  82. 82.Clarkson, K.L. A randomized algorithm for closestpoint queries, SIAM J. Comput., 17 (1988), 830-847.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  83. 83.Clarkson, K.L. Las Vegas algorithm for linear programming when the dimension is small, Proc. 29th Ann. IEEE Syrup. Foundat. Comput. Sci. (1988), 452-457.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  84. 84.Clarkson, K.L. Safe and effective determinant evaluatzon, Proc. 33rd Ann. IEEE Symp. Foundat. Comput. Sci. (1992), 387-395.]]Google ScholarGoogle Scholar
  85. 85.Clarkson, K.L. Randomized geometric algorithms, in Computing in Euclidean Geometry, D.-Z. Du and F.K. Kwang ed., Lecture Notes Series on Comput. 1 (1992), World Scientific, 117-162.]]Google ScholarGoogle Scholar
  86. 86.Clarkson, K.L., Edelsbrunner, H., Guibas, L. J., Sharir, M., Welzl, E. Combinatorial complexity bounds for arrangements of curves and spheres, Disc. Comput. Geom., 5 (1990), 99-160.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  87. 87.Clarkson, K.L., Mehlhorn, K., Seidel, R. Four results on randomized incremental constructions, Proc. 9th Symp. Theoret. Aspects Comput. Sci., LNCS 577, Springer-Verlag (1992), 463-474.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  88. 88.Clarkson, K.L., Shot, P.W. Applications of random sampling in computational geometry, H, Disc. Comput. Geom., 4 (1989), 387-421.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  89. 89.Clarkson, K.L., Tarjan, R.E., Van Wyk, C.J. A fast Las Vegas algorithm for triangulating a simple polygon, Disc. Comput. Geom., 4 (1989), 423-432.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  90. 90.Cohen, E., Megiddo, N. Strongly polynomial-time and NC algorithms for detecting cycles zn dynamic graphs, Proc. 21st ACM Syrup. Theory Comput. (1989), 523- 534.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  91. 91.Cohen# M.# WMlace# J.# Radios,fy and Realistic Image Synthesis, Academic Press, 1993.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  92. 92.Cole, R. Searching and storing similar lists, J. Algorithms, 7 (1986), 202-220.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  93. 93.Cole, R. Slowing down sorting networks to obtain faster sorting algorithms, J. ACM, 34 (1987), 200-208.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  94. 94.Cole, R., Salowe, J., Steiger, W., Szemer#di, E. An optimal-time algorithm for slope selection, SIAM J. Comput., 18 (1989), 792-810.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  95. 95.Cole, R., Sharir, M. Visibility problems for polyhedral terrains, J. Symbolic Comput., 7 (1989), 11-30.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  96. 96.Cole, R., Sharir, M., Yap, C.K. On k.hulls and related problems, SIAM J. Comput., 16 (1987), 61-77.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  97. 97.Collins, G.E. Quantifier elimination for real closed fields by cylindric algebraic decomposition, Proc. 2nd GI Conf. on Automata Theory and Formal Languages, Springer-Verlag, LNCS 35, Berlin (1975), 134-183.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  98. 98.Cox, D., Little, J., O'Shea, D. Ideals, Varieties, and Algorithms, Springer-Verlag, 1992.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  99. 99.Crapo, H., Ryan, 3. Scene analysis and geometric homology, Proc. 2nd Ann. ACM Symp. Comput. Geom. (1986), 125-132.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  100. 100.Davenport, J. and Heintz, J. Real quantifier elimination is doubly exponential, J. Symbolic Comput., 5 (1988), 29-35.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  101. 101.Delfinado, C.J.A., Edelsbrunner, H. An incremental algorithm for betti numbers of simplicial complexes, Proc. 9th Ann. ACM Syrup. Comput. Geom. (1993), 232-239.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  102. 102.Devillers, O. Randomization yields simple O(n log* n) algorithms for difficult w(n) problems, Int. J. Comput. Geom. Appl., 2 (1992), 97-111.]]Google ScholarGoogle ScholarCross RefCross Ref
  103. 103.Devillers, O., Meiser, S., Teillaud, M. Fully dynamic Delaunay triangulation in logarithmic expected time per operation, Comput. Geom. Theory Appl., 2 (1992), 55- 80.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  104. 104.Dey, T.K. Triangulation and CSG representation of polyhedra with arbitrary genus, Proc. 7th Ann. ACM Syrup. Comput. Geom. (1991), 364-372.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  105. 105.Dey, T. Optimal algorithms to detect null-homologous cycles on 2-manifolds, Proc. 5th Canad. Conf. Compu,t. Geom. (1993), 273-278.]]Google ScholarGoogle Scholar
  106. 106.Dobkin, D.P., Kirkpatrick, D.G. Fast detection ofpolyhedral intersection, Theoret. Comput. Sci., 27 (1983), 241-253.]]Google ScholarGoogle ScholarCross RefCross Ref
  107. 107.Dobkin, D.P., Silver, D., Recipes for geometry and numerical analysis-part 1: an empirical study, Proc. 4th Ann. Symp. Comput. Geom. (1988), 93-105.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  108. 108.Donald, B.R. A geometric approach to error detection and recovery for robot motion planning with uncertainty, Artif. Intell., 37 (1988), 223-271.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  109. 109.Donald, B.R., Chang, D.R. On the complexity of computing the homology type of a triangulation, Proc. 32nd Ann. IEEE Symp. Foundat. Comput. Sci. (1991), 650- 662.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  110. 110.Donald, B.R., Xavier, P., Canny, J., Reif, J. On the complexity of kinodynamic planning, J. ACM, 40 (1993), 1048-1066.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  111. 111.Dyer, M.E. On a multidimensional search technique and its application to the Euclidean 1.centre problem, SIAM J. Comput., 15 (1986), 725-738.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  112. 112.Dyer, M.E. A class of convex programs with applications to computational geometry, Proc. 8th Ann. ACM Symp. Comput. Geom. (1992), 9-15.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  113. 113.Dyer, M.E., Frieze, A.M. A randomized algorithm for fixed-dimensional linear programming, Mathematical Programming, 44 (1989), 203-212.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  114. 114.Edelsbrunner, H. Algorithms in Combinatorial Geometry, Springer-Verlag, 1987.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  115. 115.Edelsbrunner, H. The union of balls and its dual shape, Proc. 9th Ann. ACM Symp. Comput. Geom. (1993), 218-231.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  116. 116.Edelsbrunner, H., Guibas, L.J., Hershberger, 3., Seidel, R., Sharir, M., Snoeyink, J., Welzl, E. Implicitly representing arrangements of lines or segments, Disc. Comput. Geom., 4 (1989), 433-466.]]Google ScholarGoogle Scholar
  117. 117.Edelsbrunner, H., Guibas, L.J., Sharir, M. The complexity and construction of many faces ,n arrangements of lines and segments, Disc. Comput. Geom., 5 (1990), 161-196.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  118. 118.Edelsbrunner, H., Guibas, L.J., Sharir, M. The complexity of many cells in arrangements o.f planes and related problems, Disc. Comput. Geom., 5 (1990), 197- 216.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  119. 119.Edelsbrunner, H., Guibas, L.J., Stolfi, J. Optimalpoint location in a monotone subdivision, SIAM J. Comput., 15 (1986), 317-340.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  120. 120.Edelsbrunner, H., Miicke, E. Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms, ACM Trans. Graphics, 9 (1990), 66-104.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  121. 121.Edelsbrunner, H., Seidel, R. Voronoi dliagrams and arrangements, Disc. Comput. Geom., 1 (}986), 25-44.]]Google ScholarGoogle Scholar
  122. 122.Edelsbrunner, H., Seidel, R., Sharir, M. On the zone theorem for hyperplane arrangements, SIAM J. Comput., 22 (1993), 418-429.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  123. 123.Edelsbrunner, H., Shah, N. R. Triangulating topological spaces, Proc. 10th Ann. ACM Symp. Comput. Geom. (1994), to appear.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  124. 124.Emiris, I., Canny, J. A general approach to removing degeneracies, Proc. 32nd Ann. Symp. Foundat. Cornput. Sci. (1991), 405-413.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  125. 125.Erickson, J., Seidel, R. Better lower bounds on detecting al'fine and spherical degeneracies, Proc. 34th Ann. IEEE Symp. Foundat. Comput. Sci. (1993), 528-536.]]Google ScholarGoogle Scholar
  126. 126.Fitchas, N., Galligo, A., Morgenstern, J. Algorithmes rap#cles en#eque" nt#el et en parallel 29o,,r l#,#l;m;nat;on de quantificateurs en ggomdtrie dldmentaire, S#minaire Structures Ordonn#es, U.E.R. Math. Univ. Paris VII, 1987.]]Google ScholarGoogle Scholar
  127. 127.Fortune, S. A sweepline algorithm }or Voronoi diagrams, Algorithmica, 2 (1987), 153-174.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  128. 128.Fortune, S. Stable maintenance of point-set triangulation in two dimensions, manuscript, AT&T Bell Laboratories. Abbreviated version appeared in: Proc. 30th Ann. Syrup. Foundat. Comput. Sci. (1989), 494-499.]]Google ScholarGoogle Scholar
  129. 129.Fortune, S. Numerical stability o} algorithms for 2 d Delaunay triangulations and Vovonoi diagrams, Proc. 8th Ann. ACM Syrup. Comput. Geom. (1992), 83-92.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  130. 130.Fortune, S. Voronoi diagrams and Delaunay triangulatzons, in: Computing in Euclidean Geometry, eds: D.-Z. Du, F. Hwang, 1, World Scientific (1992), 193- 233.]]Google ScholarGoogle Scholar
  131. 131.Fortune, S. Computational Geometry, ed. R. Martin, Directions in Computational Geometry, Information Geometers, to appear.]]Google ScholarGoogle Scholar
  132. 132.Fortune, S., Milenkovic, V. Numerical stability of algorithms .for line arrangements, Proc. 7th Ann. Symp. Comput. Geom. (1991), 334-341.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  133. 133.Fortune, S., Van Wyk, C. J. Efficient exact arithmetic Syrup. Comput. Geom. (1993), 163-172.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  134. 134.Fredman, M.L. A lower bound on the complexity of orthogonal range queries, J. ACM, 28 (1981), 696-705.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  135. 135.Fredman, M.L. Lower bounds on the complexity of some optimal data structures, SIAM J. Comput., 10 (1981), 1-10.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  136. 136.Freedman, M.H. Identi/ying attractors via homology: a manuscript, 1991.]]Google ScholarGoogle Scholar
  137. 137.G#rtner, B. A subexponential algomthm }or abstract optzmization problems, Proc. 33rd Ann. IEEE Syrup. Foundat. Comput. Sci. (1992), 464-472.]]Google ScholarGoogle Scholar
  138. 138.Garey, M.R., Johnson, D.S., Preparata, F.P., Tarjan, R.E. Triangulating a simple polygon, Inform. Process. Lett., 7 (1978), 175-180.]]Google ScholarGoogle ScholarCross RefCross Ref
  139. 139.Glassner, A.S. Ray Tracing, Academic Press, 1989.]]Google ScholarGoogle Scholar
  140. 140.Goodman, J.E., Pollack, R. Multidimensional sorting, SIAM J. Comput., 12 (1983), 484-507.]]Google ScholarGoogle ScholarCross RefCross Ref
  141. 141.Goodman, J.E., Pollack, R. Upper bounds .for configurations and polytopes in 1##, Disc. Comput. Geom., 1 (1986), 219-227.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  142. 142.Goodman, J.E., Pollack, R., Sturmfels, B. The intrinsic spread o/ a configuration is R#, J. Amer. Math. Soc., 3 (1990), 639-651.]]Google ScholarGoogle Scholar
  143. 143.Goodman, J.E., Pollack, R., Wenger, R. Geomett:ic transversal theory, in: New Trends in Discrete and Computational Geometry, ed. J. Pach, Algorithms and Combinatorics, 10, Springer-Verlag (1993), 163-198.]]Google ScholarGoogle Scholar
  144. 144.Goodrich, M.T. Planar separators and parallel polygon triangulation, Proc. 24th Ann. ACM Syrup. Theory Comput. (1992), 507-516]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  145. 145.Goodrich, M. T. Constructing arrangements optimally in parallel, Disc. Comput. Geom., 9 (1993), 371-385.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  146. 146.Goodrich, M. T., Atallah, M. J., Overmars, M. H. Output-sensitive methods for rectilinear hidden surface removal, Inform. Comput., 107 (1993), 1-24.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  147. 147.Goodrich, M.T., Tamassia, R. Dynamic trees and dynamic point locatzon, Proc. 23rd Ann. ACM Syrup. Theory Comput. (1991), 523-533.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  148. 148.Goodrich, M.T., Tamassia, R. Dynamic ray shooting and shortest paths via balanced geodesic triangulations, Proc. 9th Ann. ACM Symp. Comput. Geom. (1993), 318-327.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  149. 149.Graham, R.L. An efficient algorithm for determining the convex hull of a planar point set, Inform. Process. Lett., 1 (1972), 132-133.]]Google ScholarGoogle ScholarCross RefCross Ref
  150. 150.Greene, D., Yao, F. Finite-resolution computational geometry, Proc. 27th Ann. Symp. Foundat. Comput. Sci. (1986), 143-152.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  151. 151.Grigor'ev, D. Complexity of deciding Tarski algebra, J. Symbolic Comput., 5 (1988), 37-64.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  152. 152.Grigor'ev, D. and Vorobjov, N. Solving systems of polynomial inequalities in subexponential time, J. Symbolic Comput., 5 (1988), 37-64.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  153. 153.Guibas, L.J., Knuth, D.,E., Sharir, M. Randomized incremental construction of Delaunay and Voronoi diagrams, Algorithmica, 7 (1992), 381-413.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  154. 154.Guibas, L.J., Overmars, M., Sharir, M. Ray shooting, implicit point location, and related queries in arrangements of segments, Tech. Rep. 433, New York Univ., March 1989.]]Google ScholarGoogle Scholar
  155. 155.Guibas, L.J., Salesin, D., Stolfi, J., Epsilon geometry: building robust algorithms from imprecise computations, Proc. 5th Ann. Symp. Comput. Geom. (1989), 208-217.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  156. 156.Guibas, L.J., Sharir, M. Combinatorics and algomthms of arrangements, New Trends in Discrete and Computational Geometry, J. Pach, ed., 1993, Springer-Verlag, 9-#6.]]Google ScholarGoogle Scholar
  157. 157.Halperin, D., Sharir, M. New bounds for lower envelopes in three dimensions, with applications to visibility in terrains, Proc. 9th Ann. ACM Syrup. Comput. Geom. (1993), 11-18.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  158. 158.I-Ialperin, D., Sharir, M. Almost tight upper bounds for the single cell and zone problems in three dimensions, Proc. 10th Ann. ACM Symp. Comput. Geom. (1994), to appear.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  159. 159.Hart, S., Sharir, M. Nonlinearity o} Davenport- Schinzel sequences and of generalized path compression schemes, Combinatorica, 6 (1986), 151-177.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  160. 160.Haussler, D., Welzl, E. e-nets and simplex range queries, Disc. Comput. Geom., 2 (1987), 127-151.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  161. 161.Heintz, J., Roy, M.-F., Solern6, P. On the complexity of semi-algebraic sets, Proc. IFIP San Francisco, North- Holland (1989), 293-298.]]Google ScholarGoogle Scholar
  162. 162.Heintz, J., Roy, M.-F., Solern6, P. Sur la complexitd du principe de Tarskz.Seidenberg, Bull. Soc. Math. France, 118 (1990), 101-126.]]Google ScholarGoogle ScholarCross RefCross Ref
  163. 163.Heintz, J., Recio, T., Roy, M.-F. Algorithms in real algebraic geometry and applications to computational geometry, Discrete and Computational Geometry, Dim#cs Series 6, AMS-ACM, ed. J.E. Goodman, R. Pollack, W. Steiger (1991), 137-163.]]Google ScholarGoogle Scholar
  164. 164.Hershberger, J., Suri, S. A pedestrian approach to ray shooting: shoot a ray, take a walk, Proc. 4th ACM- SIAM Syrup. Disc. Alg. (1993), 54-63.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  165. 165.Hoffmann, C. Geometric and Solid Modeling, Morgan Kaufmann, 1989.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  166. 166.Hoffmann, C. Hopcroft, J., Karasick, M. Towards ,mplementing robust geometric computations, Proc. 4th Ann. Syrup. Comput. Geom. (1988), 106-117.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  167. 167.Hoffmann, C., Hopcroft, J., Karasick, M. Robust set operations on polyhedral solids, IEEE Comput. Graph. Appl., 9 (1989), 50-59.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  168. 168.Hopcroft, J., Wilfong, G. Reducing multiple object motion planning to graph searching, SIAM J. Comput., 15 (1986), 768-785.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  169. 169.Huttenlocher, D. P. Three-Dzmensional Recognition of Solid Objects from a Two-Dimensional Image, Ph.D. Thesis, MIT, Report TR-1045, 1988.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  170. 170.Impagliazzo, R., Zuckerman, D. How to recycle random bits, Proc. 30th Ann. IEEE Syrup. Foundat. Comput. Sci. (1989), 248-253.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  171. 171.Kalai, G. A subexponential randomized simplex algomthm, Proc. 24th Ann. ACM Symp. Theory Comput. (1992), 475-482.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  172. 172.Karasick, M., Lieber, D., Nackman, L. Efficient Delaunay triangulation using rational arithmetic, ACM Trans. Graphics, 10 (1990), 71-91.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  173. 173.Karasick, M. On the representation and manipulation of rigid solids, Ph.D. thesis, McGill U., 1988.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  174. 174.Katz, M., Sharir, M. Optimal slope selection via expanders, Proc. 5th Canad. Conf. Comput. Geom. (a998), 139-144.]]Google ScholarGoogle Scholar
  175. 175.Kirkpatrick, D.G. Optimal search in planar subdivisions, SIAM J. Comput., 12 (1983), 28-35.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  176. 176.Kirkpatrick, D.G., Klawe, M.M., Tarjan, R.E. Polygon triangulation in O(nloglogn) time with simple data structures, Disc. Comput. Geom., 7 (1992), 329-346.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  177. 177.Kirkpatrick, D.G., Seidel R. The ultimate planar convex hull algomthm? SIAM J. Comput., 15 (1986), 287- 299.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  178. 178.Klein, R. Abstract Voronoi diagrams and their applications, Computational Geometry and its Applications, LNCS 333, Springer-Verlag (1988), 148-157.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  179. 179.Li, Z., Milenkovic, V. Constructing strongly convex hulls using exact or rounded arithmetic, Proc. 6th Ann. Syrup. Comput. Geom. (1990), 235-243.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  180. 180.Lipton, R.J., Tarjan, R.E. Applications of a planar separator theorem, SIAM 3. Comput., 9 (1980), 615- 627.]]Google ScholarGoogle Scholar
  181. 181.Lo, C.-Y, Matou#ek, J., Steiger, W. Ham-sandwzch cuts in Ra, Proc. 24th Ann. ACM Symp. Theory Comp,t. (1992), 839-545.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  182. 182.Luby, M. A simple parallel algorithm .for the maximal independent set problem, Proc. 17th Ann. ACM Symp. Theory Comput. (1985), 1-10.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  183. 183.Matou#ek, J. Construction of e-nets, Disc. Comput. Geom., 5 (1990), 427-448.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  184. 184.Matougek, J. Cutting hyperplane arrangements, Disc. Comput. Geom., 6 (1991), 385-406.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  185. 185.Matou#ek, J. Approximations and optimal geometric divide-and-conquer, Proc. 23rd ACM Syrup. Theory Comput. (1991), 506-511.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  186. 186.Matou#ek, J. Range searching with efficient h,erarchical cuttings, Disc. Comput. Geom., 10 (1993), 157-182.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  187. 187.Matou#ek, J. Efficient partition trees, Disc. Comput. Geom., 8 (1992), 315-334.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  188. 188.Matou#ek, J. Reporting points in halfspaoes, Comput. Geom. Theory Appl., 2 (1992), 169-186.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  189. 189.Matou#ek, J. Linear optimization queries, J. Algorithms, 14 (1993), 432-448.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  190. 190.Matou#ek, J. Geometric range searching, Tech. Report B-93-09, Free Univ. Berlin, 1993.]]Google ScholarGoogle Scholar
  191. 191.Matou#ek, J., Schwarzkopf, O. A deterministic algorithm for the three-dimensional diameter problem, Proc. 25th Ann. ACM Symp. Theory Comput. (1993), 478-484.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  192. 192.Matou#ek, J., Schwarzkopf, O. On ray ,:hooting in convex polytopes, Disc. Comput. Geom., 10 (1993), 215- 232.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  193. 193.Matou#ek, J., Sharir, M., Welzl, E. A subexponential bound for linear programming, Proc. 8th ACM Syrup. Comput. Geom. (1992), 1-8. To appear in Algorithmica.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  194. 194.Matou#ek, J., Welzl, E., Wernisch, L. Discrepancy and e-approximations for bounded VC-dimension# Combinatorica, 13 (1993), 455-466.]]Google ScholarGoogle Scholar
  195. 195.Megiddo, N. Combinatorial optimization with rational objective functions, Mathematics of Operations Iresearch, 4 (1979), 414-424.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  196. 196.Megiddo, N. Applying parallel computation algorithms in the design of serial algorithms, J. ACM, 30 (1983), 852-865.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  197. 197.Megiddo, N. Linear programming in linear time when the dimension is fixed, J. ACM, 31 (1984), 114-127.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  198. 198.Mehlhorn, K. Data Structures and Algorithms 3: Multidimensional Searching and Computational Geometry, Springer-Verlag, Heidelberg, Germany, 1984.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  199. 199.Mehlhorn, K., Simon, K. Intersecting two polyhedra one of which is convex, Proc. Foundat. Comput. Theory, LNCS 199, Springer-Verlag (1985), 534-542.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  200. 200.Mehlhorn, K., Yap, C.K. Constructive Whitney- Graustein theorem, or how to untangle closed planar curves, SIAM J. Comput., 20 (1991), 603-621.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  201. 201.Milenkovic, V. Verifiable implementations of geometric algorithms using finite precision arithmetic, Artificial Intelligence, 37 (1988), 377-401.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  202. 202.Milenkovic, V. Verifiable Implementations of Geometric Algorithms using Finite Precision Arithmetic, Ph.D. Thesis, Carnegie-Mellon, 1988. Technical Report CMU-CS-88-168, Carnegie Mellon University, 1988.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  203. 203.Milenkovic, V. Double precision geometry: a general technique for calculating line and segment intersections using rounded arithmetic, Proc. 30th Ann. IEEE Symp. Foundat. Comput. Sci. (1989), 500-505.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  204. 204.Milenkovic, V. Rounding face lattices in the plane, Abstracts 1st Canad. Conf. Comput. Geom. (1989), 12.]]Google ScholarGoogle Scholar
  205. 205.Milenkovic, V. Rounding face lattices in d dimensions, Proc. 2nd Canad. Conf. Comput. Geom. (1990), 40-45.]]Google ScholarGoogle Scholar
  206. 206.Mishra, B. Algorithmic Algebra, Springer-Verlag New York, Inc., 1993.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  207. 207.Mitchell, $., Vavasis, S. Quality mesh generation in three dimensions, Froc. 8th Ann. ACM Symp. Comput. Geom. (1992), 212-221.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  208. 208.Motwani, R., Naor, J., Naor, M. The probab#listic method yields deterministic parallel algorithms, Proc. 30th Ann. IEEE Syrup. Foundat. Comput. Sci. (1989), 8-13.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  209. 209.Muller, D.E., Preparata, F.P. Finding the intersection of two convex polyhedra, Theoret. Comput. Sci., 7 (1978), 217-236.]]Google ScholarGoogle ScholarCross RefCross Ref
  210. 210.Mulmuley, K. A fast planar partition algorithm 1, Proc. 29th Ann. IEEE Syrup. Foundat. Comput. Sci. (1988), 580-589.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  211. 211.Mulmuley, K. On obstructions in relation to a fixed viewpoint, Proc. 30th Ann. IEEE Symp. Foundat. Comput. Sci. (1989), 592-597.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  212. 212.Mulmuley, K. On levels in arrangements and Voronoi diagrams, Disc. Comput. Geom., 6 (1990), 307-338.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  213. 213.Mulmuley, K. A fast planar partition algorithm II, 3. ACM, 38 (1991), 74-103.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  214. 214.Mulmuley, K. Hidden surface removal with respect to a moving point, Proc. 23rd Ann. ACM Syrup. Theory Comput. (1991), 512-522.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  215. 215.Mulmuley, K. Randomized multidimensional search trees: dynamic sampling, Proc. 7th Ann. ACM Symp. Comput. Geom. (1991), 121-131.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  216. 216.Mulmuley, K. Randomized multidimensional search trees: lazy balancing and dynamic shuffling, Proc. 32nd IEEE Ann. Syrup. Foundat. Comput. Sci. (1991), 180- 194.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  217. 217.Mulmuley, K. Randomized multidimensional search trees: further results in dynamic sampling, Proc. 32nd IEEE Ann. Symp. Foundat. Comput. Sci. (1991), 216- 227.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  218. 218.Mulmuley, K. Randomized geometric algorithms and pseudo-random generators, Proc. 33rd Ann. IEEE Syrup. Foundat. Comput. Sci. (1992), 90-100.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  219. 219.Mulmuley# K. Computational Geometry: An Introduction Through Randomized Algorithms, Prentice-Hall, 1994.]]Google ScholarGoogle Scholar
  220. 220.Naor, J., Naor, M. Small-bias probability spaces: efficient constructions and applications, Proc. 22nd Ann. ACM Syrup. Theory of Comput. (1990), 213-223.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  221. 221.Norton, C.H., Plotkin, S.A., Tardos, E. Using separation algorithms in fixed dimensions, j. Algorithms, 13 (1992), 79-98.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  222. 222.O'Rourke, J. Art Gallery Theorems and Algorithms, Oxford Univ. Press, New York, NY (1987).]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  223. 223.O'Rourke, J. Computational G#om#try in C, Cambridge Univ. Press, 1994.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  224. 224.Pach, J., Agarwal, P.K. Combinatorial Geometry, John Wiley & Sons, in press.]]Google ScholarGoogle Scholar
  225. 225.Pach, J., Steiger, W., Szemer6di, E. An upper bound on the number of planar k-sets, Disc. Comput. Geom., 7 (1992), 109-123.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  226. 226.Pellegrini, M. Ray shooting on triangles in 3- dimensional space, Algorithmica, 9 (1993), 471-494.]]Google ScholarGoogle ScholarCross RefCross Ref
  227. 227.Pellegrini, M. On point location and motion planning among simplices, these proceedings.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  228. 228.Poll#ck, R., Roy, M.-F. On the number of cells defined by a set of polynomials, Compte-Rendus, 316 (1993), 573-577.]]Google ScholarGoogle Scholar
  229. 229.Preparata, F.P., Hang, S.J. Convex hulls of finite sets of points in two and three dimensions, Comm. ACM, 20 (#977), 87-93.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  230. 230.Prepatata, F.P, Shamos, M.I. Computational Geome. try: an lntroductzon, Springer-Verlag, New York, 1988.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  231. 231.Preparata, F.P., Tamassia, R. Fully dynamic techniques for point location and transitive closure in planar structures, Proc. 29th Ann. IEEE Symp. Foundat. Comput. Sci. (1988), 558-567.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  232. 232.Prepar#t#, F.P., Tamassia, R. Efficient point location in a convex spatial cell-complex, SIAM J. Comput., 21 (1992), 267-280.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  233. 233.Prill, D. On approximations and incidenoe in cylindrical algebraic decompositions, SIAM J. Comput., 15 (1986), 972-993.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  234. 234.Raghavan, P. Probabilistzc construction of determirtistzc algorithms: Approximating packin9 integer programs, J. Comput. System Sci., 37 (1988), 130-143.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  235. 235.Ramos, E., Intersection of unit-balls and diameter of a set of points in R3, manuscript, 1994.]]Google ScholarGoogle Scholar
  236. 236.Reif, J.H., Sen, S. Optimal randomized parallel algorithms for computational geometry, Algorithmica, 7 (1992), 91-117.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  237. 237.Renegar, J. On the computational complexity and geometry of the first order theory of the reals, I, iI, II}, J. Symbolic Comput., 13 (1992), 255-352.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  238. 238.Ruppert, J., Seidel, R. On the difficulty of triangulating three-dimensional non-convex polyhedra# Disc. Comput. Geom., 7 (1992), 227-253.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  239. 239.Saalfeld, A. Divide_and_conquer in early algebraic topology: the Mayer-Vietoris exact homology sequence revisited, Abstracts 1st Canad. Conf. Comput. Geom. (1989), 11.]]Google ScholarGoogle Scholar
  240. 240.Sarn#k, N., Tarjan, R.E. Planar point location using persistent search trees, Comm. ACM, 29 (1986), 669- 679.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  241. 241.Schipper, it. Determining contractibility of curves, Proc. 8th Ann. ACM Syrup. Comput. Geom. (1992), 358-367.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  242. 242.Schwartz, J.T., Sharir, M. On the "piano movers" problem. II: General techniques for computing topological properties of real algebraic manifolds, Adv. in Appl. Math., 4 (1983), 298-35.1.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  243. 243.Schwartz, J.T., Sharir, M. Algorithmzc motion plannzng in robotzcs, in: Algorithms and Complexity, Handbook of Theoretical Computer Science, ed. J. van Leeuwen, Vol. A, Elsevier (1990), 391-430.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  244. 244.Seidel, R. A convex hull algorithm optimal for point sets in even dimensions, Univ. British Columbia, tech. Rep. 81-14, 1981.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  245. 245.Seidel, R. Constructing higher-dimensional convex hulls at logarithmzc cost per face, Proc. 18th Ann. ACM Symp. Theory Comput. (1986), 404-413.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  246. 246.Seidel, R. Small-dimensional linear programming and convex hulls made easy, Disc. Comput. Geom., 6 (1991), 423-434.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  247. 247.Seidel, R. A simple and fast increraental randomized algorithm for computing trapezoidal decompositions and for triangulating polygons, Comput. Geom. Theory Appl. 1 (1991), 51-64.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  248. 248.Seidel, R. Backward analysis of randomized geometric algorithms, New Trends in Discrete and Computational Geometry, J. Pach, ed., 1993, Springer-Verlag, 37-67.]]Google ScholarGoogle Scholar
  249. 249.Seidel, R. The nature and meaning of perturbations zn geometric computing, manuscript, 1994.]]Google ScholarGoogle Scholar
  250. 250.Shamos, M.I., Hoey, D. Closest-point .problems, Proc. 16th Ann. IEEE Symp. Foundat. Comput. Sci. (1975), 151-162.]]Google ScholarGoogle Scholar
  251. 251.Sharir, M. Almost tight upper bound,, for lower envelopes in higher dimensions, Proc. 34th Ann. IEEE Symp. Foundat. Comput. Sci. (1993), 498-507.]]Google ScholarGoogle ScholarDigital LibraryDigital Library
  252. 252.Sharir, M., Agarwal, P.K. Davenport-Schinzel Sequences and Their Geometric Applications, Cambridge Univ. Press, to #ppear.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  253. 253.Sharir, M., Welzl, E. A combinatorial bound for linear programming and related problems, Proc. 9th Symp. Theoret. Aspects of Comput. Sci. LNCS 577 (1992), 569-579.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  254. 254.Spencer, J.H. Ten Lectures on the Probabzhstic Method, CBMS-NSF, SIAM, 1987.]]Google ScholarGoogle Scholar
  255. 255.Sugihara, K., Iri, M. Construction of the Voronoi diagram for one milhon generators in single precision arithmetic, First Canad. Conf. Comput. Geom., 1989.]]Google ScholarGoogle Scholar
  256. 256.Sugihara, K., Iri, M. A sohd modeling system free from topological znconsistency, J. Information Processing, Information Processing Society of Japan, 12 (1989), 380-393.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  257. 257.Tarjan, R.E., Van Wyk, C.J. An O(nloglogn)-tzme algorithm for tr'#angttlat#ng a simple polygon, 9IAM J. Comput., 17 (1988), 143-178.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  258. 258.Tourlakis, G., Mylopoulos, J. Some results in computational topology, J. ACM, 20 (1973), 439-455.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  259. 259.Vaidya, P.M., Space-time tradeoffs for orthogonal range queries, SIAM J. Comput., 18 (1989), 748-758.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  260. 260.Vapnik, V.N., Chervonenkis, A. Ya. On the uniform convergence of relative frequencies of events to their probabilities, Theory Probab. Appl., 16 (1971), 264- 280.]]Google ScholarGoogle ScholarCross RefCross Ref
  261. 261.Vegter, G. Kink-free deformations of polygons, Proc. 5th Ann. ACM Syrup. Comput. Geom. (1989), 61-68.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  262. 262.Vegter, G., Yap, C.K. Computational complexity of combinatorial surfaces, Proc. 6th Ann. ACM Symp. Coraput. Geom. (1990), 102-111.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  263. 263.Weispfenning, V. The complexity of linear problems in fields, J. Symbolic Comput., 5 (1988), 3-27.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  264. 264.Welzl, E. Partition trees :for triangle counting and other range searching problems, Proc. 4th Ann. ACM Syrup. Comput. Geom. (1988), 23-33.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  265. 265.Welzl, E., On spanning trees with low crossing numbers, Tech. Rep. TR B 92-02, Free University, Berlin, 1992.]]Google ScholarGoogle ScholarCross RefCross Ref
  266. 266.Whitney, H. Elementary structure of real algebraic va. rieties, Annals of Math., 66 (1957).]]Google ScholarGoogle Scholar
  267. 267.Willard, D.E. Polygon retrieval, SIAM J. Comput., 11 (1982), 149-165.]]Google ScholarGoogle ScholarCross RefCross Ref
  268. 268.Y#o, A.C. On the complexity of maintaining partial sums, SIAM J. Comput., 14 (1985), 277-288.]]Google ScholarGoogle ScholarCross RefCross Ref
  269. 269.Y#o, A.C. A lower bound to finding convex hulls, J. ACM, 28 (1981), 780-787.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  270. 270.Y#o, A.C. Lower bounds for algebraic computation trees with integer inputs, Proc. 30th Ann. IEEE Syrup. Foundat. Comput. Sci. (1989), 308-313.]]Google ScholarGoogle Scholar
  271. 271.Y#o, F.F. Computational Geometry, in: Algorithms and Complexity, Handbook of Theoretical Computer Science, ed. J. w# Leeuwen, Vol. A, Elsevier (1990), 343-389.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  272. 272.Y#o, A.C., Y#o, F.F. A general approach to ddimensional geometric queries, Proc. 17th Ann. ACM Syrup. Theory of Comput. (1985), 163-168.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  273. 273.Y#p, C.K. Symbolic treatment of geometric degeneracies, J. Symbolic Comput., 10 (1990), 349-370.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  274. 274.Y#p, C.K. A geometric consistency theorem for a symbolic perturbation scheme, J. Comput. Sys. Sci., 40 (1990), 2-18.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  275. 275.Yap, C.K. Towards exact geometric computation, Proc. 5th Canad. Conf. Comput. Geom. (1993), 405- 419.]]Google ScholarGoogle Scholar

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                STOC '94: Proceedings of the twenty-sixth annual ACM symposium on Theory of Computing
                May 1994
                822 pages
                ISBN:0897916638
                DOI:10.1145/195058

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