Computational geometry: A retrospective

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn Part F129502, Issue , 1994, Pages 75-94

  Chazelle, Bernard ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; COMPUTATIONAL GEOMETRY; GEOMETRY; ALGORITHMS; COMPUTATION THEORY; COMPUTATIONAL METHODS; SAMPLING; TOPOLOGY;

APPLIED MATHEMATICS; COMPUTATIONAL REAL ALGEBRAIC GEOMETRY; COMPUTATIONAL TOPOLOGY; FINITE PRECISION; GEOMETRIC ALGORITHM; GEOMETRIC COMPUTING; SCIENTIFIC ACHIEVEMENTS; SUB-AREAS;

COMPUTATION THEORY; GEOMETRY;

COMPUTATIONAL GEOMETRY; COMPUTATIONAL TOPOLOGY; GEOMETRIC SAMPLING; VORONOI DIAGRAMS;

EID: 0027929096     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/195058.195110     Document Type: Conference Paper

References (275)

1. Agarwal, P.K. Partitioning arrangements of lines II: Applications, Disc. Comput. Geom., 5 (1990), 533-573.
2. Agarwal, P.K. Ray shooting and other applications of spanning trees with low stabbing number, SIAM J. Corn- put., 22 (1992), 540-570.
3. Agarwal, P.K., Arcmov, B. Counting facets and incidences, Disc. Comput. Geom., 7 (1992), 359-369.
4. Agarwal, P.K., Matousek, J. Ray shooting and parametric search, SIAM J. Comput., 22 (1993), 794-806.
5. Agarwal, P.K., Matousek, J. Range searching with semialgebraic sets, Disc. Comput. Geom. (1994), in press.
6. Agarwal, P.K., Sharir, M. Application of a new space partitioning technique, Disc. Comput. Geom., 9 (1993), 11-38.
7. Agarwal, P.K., Sharir, M., Shor, P. Sharp upper and lower bounds on the length of general Davenport- Schinzel sequences, J. Combin. Theory Ser. A, 52 (1989), 228-274.
8. Agarwal, P.K., Sharir, M., Toledo, S. Applications of parametric searching in geometric optimization, Proc. 3rd ACM-SIAM Symp. Disc. Alg. (1992), 72-82.
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..
10. Aggarwal, A., Chazelle, B., Guibas, L.J., O'Dunlaing, C., Yap, C.K. Parallel computational geometry, Algo- rithmica, 3 (1988), 293-327.
11. Ajtai, M., Megiddo, N. A deterministic Poly(loglogN)-Time N-processor algorithm for linear programming in fixed dimension, Proc. 24th Ann. ACM Symp. Theory Comput. (1992), 327-338.
12. Alon, N., Babai, L., Itai, A. A fast and simple randomized algorithm for the maximal independent set problem, J. Algorithms, 7 (1986), 567-583.
13. Alon, N., Barany, I., Fiiredi, Z., Kleitman, D. Point selections and weak e-nets for convex hulls, Combinatorics, Probability and Computing, 3 (1992), 189-200.
14. Alon, N., Goldreich, O., Hastad, J., Peralta, R. Simple constructions of almost k-wise independent random variables, Random Structures & Algorithms, 3 (1992), 289-304.
15. Alon, N., Spencer, J.H. The Probabilistic Method, John Wiley & Sons, 1992.
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.
17. Aronov, B., Matousek, J., Sharir, M. On the sum of squares of cell complexities in hyperplane arrangements, Proc. 7th Ann. Symp. Comput. Geom. (1991), 307-313. To appear in J. Combin. Theory Ser. A.
18. Aronov, B., Pellegrini, M., Sharir, M. On the zone of a surface in a hyperplane arrangement, Disc. Comput. Geom., 9 (1993), 177-186.
19. Aronov, B., Sharir, M. Triangles in space or building (and analyzing) castles in the air, Combinatorica, 10 (1990), 137-173.
20. Aronov, B., Sharir, M. Castles in the air revisited, Proc. 8th Ann. ACM Symp. Comput. Geom. (1992), 146-156. To appear in Disc. Comput. Geom.
21. Aronov, B., Sharir, M. The union of convex polyhe- dra in three dimensions, Proc. 34th Ann. IEEE Symp. Foundat. Comput. Sci. (1993), 518-527.
22. Aurenhammer, F. Power diagrams: properties, algorithms and applications, SIAM J. Comput., 16 (1987), 78-96.
23. Aurenhammer, F. Voronoi diagrams: A survey of a fundamental geometric data structure, ACM Comput. Surv., 23 (1991), 345-405.
24. Bajaj, C.L., Dey, T.K. Convex decompositions of poly- hedra and robustness, SIAM J. Comput., 21 (1992), 339-364.
25. Basu, S., Pollack, R., Roy, M.-F. On the combinatorial and algebraic complexity of quantifier elimination, manuscript, 1994.
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.
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. Halperin, J.-C. Latombe, R.H. Wilson. To appear.
28. Beck, J. An algorithmic approach to the Lovdsz local lemma. I. Random Structures k. Algorithms, 2 (1991), 343-365.
29. Ben-Or, M. Lower bounds for algebraic computation trees, Proc. 15th Ann. ACM Symp. Theory Comput. (1983), 80-86.
30. Ben-Or, M., Kozen, D., Reif, J. The complexity of elementary algebra and geometry, J. Comput. Syst. Sci., 32 (1986), 251-264.
31. Bentley, J.L., Ottmann, T.A. Algorithms for reporting and counting geometric intersections, IEEE Trans. Comput., C-28 (1979), 643-647.
32. Berger, B., Rompel, J. Simulating (log n)c-wise independence in NC, J. ACM, 38 (1991), 1028-1046.
33. Berger, B., Rompel, J., Shor, P. Efficient NC algorithms for set cover with applications to learning and geometry, Proc. 30th Ann. IEEE Symp. Foundat. Comput. Sci., (1989), 54-59.
34. Bern, M. Compatible tetrahedralizations, Proc. 9th Ann. ACM Symp. Comput. Geom. (1993), 281-288.
35. Bern, M., Dobkin, D., Eppstein, D. Triangulating polygons without large angles, Proc. 8th Ann. ACM Symp. Comput. Geom. (1992), 222-231.
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, 23-90.
37. Bern, M., Eppstein, D., Gilbert, J. Provably good mesh generation, Proc. 31st Ann. IEEE Symp. Foundat. Comput. Sci. (1990), 231-241.
38. Bjorner, A., Lovasz, L., Yao, A.C. Linear decision trees: volume estimates and topological bounds, Proc. 24th Ann. ACM Symp. Theory Comput. (1992), 170- 177.
39. Bochnak, J., Coste, M., Roy, M.-F. Geometrie algebrique reelle, Springer Verlag, Heidelberg, 1987.
40. Boissonnat, J.D., Devillers, O., Schott, R., Teillaud, M., Yvinec, M. Applications of random sampling to online algorithms in computational geometry, Disc. Comput. Geom., 8 (1992), 51-71.
41. Boissonnat, J.D., Teillaud, M. On the randomized construction of the Delaunay tree, Theoret. Comput. Sci., 112 (1993), 339-354.
42. Bronnimann, H., Chazelle, B., Matousek, J. Product range spaces, sensitive sampling, and derandomization, Proc. 34th Ann. IEEE Symp. Foundat. Comput. Sci., 400-409.
43. Bronnimann, H., Chazelle, B., Pach, J. How hard is halfspace range searching?, Disc. Comput. Geom., 10 (1993), 143-155.
44. Canny, J. The Complexity of Robot Motion Planning, MIT Press, 1987.
45. Canny, J. Some algebraic and geometric computations in PSPACE, Proc. 20th Ann. ACM Symp. Theory Comput. (1988), 460-467.
46. Canny, J. Generalized characteristic polynomials, J. Symbolic Comput., 9 (1990), 241-250.
47. Canny, J. Some Practical Tools for Algebraic Geometry, Tech. Rep., Spring school on robot motion planning, Promotion Esprit, 1993.
48. Canny, J. Computing road maps m general semi-Algebraic sets, The Computer Journal, 36 (1993), 504514.
49. Canny, J. Improved algorithms for sign determination and existential quantifier elimination, The Computer Journal, 36 (1993), 409-418.
50. Canny, J., Donald, B.R., Ressler, G. A rational rotation method for robust geometric algorithms, Proc. 8th Ann. ACM Symp. Comput. Geom. (1992), 251-260.
51. Chazelle, B. Convex partitions of polyhedra: A lower bound and worst-case optimal algorithm, SIAM J. Comput., 13 (1984), 488-507.
52. Chazelle, B. Filtering search: A new approach to query-Answering, SIAM J. Comput., 15 (1986), 703-724.
53. Chazelle, B. Lower bounds on the complexity of polytope range searching, J. Amer. Math. Soc., 2 (1989), 637-666.
54. Chazelle, B. Lower bounds for orthogonal range searching: I. the reporting case, II. the arithmetic model, J. ACM, 37 (1990), 200-212 and 439-463.
55. Chazelle, B. Triangulating a simple polygon in linear time, Disc. Comput. Geom., 6 (1991), 485-524.
56. Chazelle, B. An optimal algorithm for intersecting three-dimensional convex polyhedra, SIAM J. Comput., 21 (1992), 671-696.
57. Chazelle, B. Cutting hyperplanes for divide-And- conquer, Disc. Comput. Geom., 9 (1993), 145-158.
58. Chazelle, B. An optimal convex hull algorithm in any fixed dimension, Disc. Comput. Geom., 10 (1993), 377409.
59. Chazelle, B., Dobkin, D.P. Optimal convex decompositions, Computational Geometry, G.T. Toussaint, ed., North-Holland (1985), 63-133.
60. Chazelle, B., Edelsbrunner, H. An optimal algorithm for intersecting line segments in the plane, J. ACM 39 (1992), 1-54.
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), 661673.
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 Symp. Theory of Comput. (1993).
63. Chazelle, B., Edelsbrunner, H., Guibas, L.J., Sharir, M. Lines in space - combinatorics, algorithms and applications, Proc. 21st Ann. ACM Symp. Theory of Comput. (1989), 382-393.
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.
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.
66. Chazelle, B., Edelsbrunner, H., Guibas, L.J., Sharir, M., Snoeyink, J. Computing a face in an arrangement of line segments and related problems, SIAM J. Comput., 22 (1993), 1286-1302.
67. Chazelle, B., Friedman, J. A deterministic view of random sampling and its use in geometry, Combinatorica, 10 (1990), 229-249.
68. Chazelle, B., Guibas, L.J. Visibility and intersection problems in plane geometry, Disc. Comput. Geom., 4 (1989), 551-581.
69. Chazelle, B., Guibas, L.J. Fractional cascading: I. A data structuring technique, II. Applications, Algorith- mica, 1 (1986), 133-162 and 163-191.
70. Chazelle, B., Matousek, J. On linear-Time deterministic algorithms for optimization problems in fixed dimension, Proc. 4th Ann. ACM-SIAM Symp. Disc. Alg. (1993), 281-290.
71. Chazelle, B., Matousek, J. Derandomizing an output- sensitive convex hull algorithm in three dimensions, Comput. Geom.: Theory and Appl. (1994), to appear.
72. Chazelle, B., Palios, L. Triangulating a nonconvex poly-Tope, Disc. Comput. Geom., 5 (1990), 505-526.
73. Chazelle, B., Rosenberg, B. Lower bounds on the complexity of simplex range reporting on a pointer machine, Proc. 19th ICALP, LNCS 623, Springer-Verlag (1992), 439-449.
74. Chazelle, B., Sharir, M. An algorithm for generalized point location and its applications, J. Symbolic Comput., 10 (1990), 281-309.
75. Chazelle, B., Sharir, M., Welzl, E. Quasi-optimal upper bounds for simplex range searching and new zone theorems, Algorithmica, 8 (1992), 407-429.
76. Chazelle, B., Shouraboura, N. Bounds on the size of tetrahedralizations, Proc. 10th Ann. ACM Symp. Comput. Geom. (1994), to appear.
77. Chazelle, B., Welzl, E. Quasi-optimal range searching in spaces of finite VC-dimension, Disc. Comput. Geom., 4 (1989), 467-489.
78. Cheng, S.W., Janardan, R. New results on dynamic planar point location, SIAM J. Comput., 21 (1992), 972-999.
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.
80. Clarkson, K.L. Linear programming in 0(nx 3d ) time, Inf. Process. Lett., 22 (1986), 21-24.
81. Clarkson, K.L. New applications of random sampling in computational geometry, Disc. Comput. Geom., 2 (1987), 195-222.
82. Clarkson, K.L. A randomized algorithm for closest- point queries, SIAM J. Comput., 17 (1988), 830-847.
83. Clarkson, K.L. Las Vegas algorithm for linear programming when the dimension is small, Proc. 29th Ann. IEEE Symp. Foundat. Comput. Sci. (1988), 452-457.
84. Clarkson, K.L. Safe and effective determinant evaluation, Proc. 33rd Ann. IEEE Symp. Foundat. Comput. Sci. (1992), 387-395.
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.
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.
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.
88. Clarkson, K.L., Shor, P.W. Applications of random sampling in computational geometry, II, Disc. Comput. Geom., 4 (1989), 387-421.
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.
90. Cohen, E., Megiddo, N. Strongly polynomial-Time and NC algorithms for detecting cycles in dynamic graphs, Proc. 21st ACM Symp. Theory Comput. (1989), 523-534.
91. Cohen, M., Wallace, J., Radioszty and Realistic Image Synthesis, Academic Press, 1993.
92. Cole, R. Searching and storing similar lists, J. Algorithms, 7 (1986), 202-220.
93. Cole, R. Slowing down sorting networks to obtain faster sorting algorithms, J. ACM, 34 (1987), 200-208.
94. Cole, R., Salowe, J., Steiger, W., Szemeredi, E. An optimal-Time algorithm for slope selection, SIAM J. Comput., 18 (1989), 792-810.
95. Cole, R., Sharir, M. Visibility problems for polyhedral terrains, J. Symbolic Comput., 7 (1989), 11-30.
96. Cole, R., Sharir, M., Yap, C.K. On k-hulls and related problems, SIAM J. Comput., 16 (1987), 61-77.
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.
98. Cox, D., Little, J., O'Shea, D. Ideals, Varieties, and Algorithms, Springer-Verlag, 1992.
99. Crapo, H., Ryan, J. Scene analysis and geometric homology, Proc. 2nd Ann. ACM Symp. Comput. Georu. (1986), 125-132.
100. Davenport, J. and Heintz, J. Real quantifier elimination is doubly exponential, J. Symbolic Comput., 5 (1988), 29-35.
101. Delfinado, C.J.A., Edelsbrunner, H. An incremental algorithm for betti numbers of simplicial complexes, Proc. 9th Ann. ACM Symp. Comput. Geom. (1993), 232-239.
102. Devillers, O. Randomization yields simple 0(n log∗ n) algorithms for difficult w problems, Int. J. Comput. Geom. Appl., 2 (1992), 97-111.
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.
104. Dey, T.K. Triangulation and CSG representation of polyhedra with arbitrary genus, Proc. 7th Ann. ACM Symp. Comput. Geom. (1991), 364-372.
105. Dey, T. Optimal algorithms to detect null-homologous cycles on 2-manifolds, Proc. 5th Canad. Conf. Compujt. Geom. (1993), 273-278.
106. Dobkin, D.P., Kirkpatrick, D.G. Fast detection of polyhedral intersection, Theoret. Comput. Sci., 27 (1983), 241-253.
107. Dobkin, D.P., Silver, D., Recipes for geometry and numerical analysis-part I: An empirical study, Proc. 4th Ann. Symp. Comput. Geom. (1988), 93-105.
108. Donald, B.R. A geometric approach to error detection and recovery for robot motion planning with uncertainty, Artif. Intell., 37 (1988), 223-271.
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.
110. Donald, B.R., Xavier, P., Canny, J., Reif, J. On the complexity of kinodynamic planning, J. ACM, 40 (1993), 1048-1066.
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.
112. Dyer, M.E. A class of convex programs with applications to computational geometry, Proc. 8th Ann. ACM Symp. Comput. Geom. (1992), 9-15.
113. Dyer, M.E., Frieze, A.M. A randomized algorithm for fixed-dimensional linear programming, Mathematical Programming, 44 (1989), 203-212.
114. Edelsbrunner, H. Algorithms in Combinatorial Geometry, Springer-Verlag, 1987.
115. Edelsbrunner, H. The union of balls and its dual shape, Proc. 9th Ann. ACM Symp. Comput. Geom. (1993), 218-231.
116. Edelsbrunner, H., Guibas, L.J., Hershberger, J., Sei- del, R., Sharir, M., Snoeyink, J., Welzl, E. Implicitly representing arrangements of lines or segments, Disc. Comput. Geom., 4 (1989), 433-466.
117. Edelsbrunner, H., Guibas, L.J., Sharir, M. The complexity and construction of many faces m arrangements of lines and segments, Disc. Comput. Geom., 5 (1990), 161-196.
118. Edelsbrunner, H., Guibas, L.J., Sharir, M. The complexity of many cells in arrangements of planes and related problems, Disc. Comput. Geom., 5 (1990), 197-216.
119. Edelsbrunner, H., Guibas, L.J., Stolfi, J. Optimal point location in a monotone subdivision, SIAM J. Comput., 15 (1986), 317-340.
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.
121. Edelsbrunner, H., Seidel, R. Voronoi diagrams and arrangements, Disc. Comput. Geom., 1 (1986), 25-44.
122. Edelsbrunner, H., Seidel, R., Sharir, M. On the zone theorem for hyperplane arrangements, SIAM J. Comput., 22 (1993), 418-429.
123. Edelsbrunner, H., Shah, N. R. Triangulating topological spaces, Proc. 10th Ann. ACM Symp. Comput. Geom. (1994), to appear.
124. Emiris, I., Canny, J. A general approach to removing degeneracies, Proc. 32nd Ann. Symp. Foundat. Comput. Sci. (1991), 405-413.
125. Erickson, J., Seidel, R. Better lower bounds on detecting affine and spherical degeneracies, Proc. 34th Ann. IEEE Symp. Foundat. Comput. Sci. (1993), 528-536.
126. Fitchas, N., Galligo, A., Morgenstern, J. Algorithmes rapiAes en sequentiel et en parallel potir I'elimination de quantificateurs en geometrie elementaire, Seminaire Structures Ordonnees, U.E.R. Math. Univ. Paris VII, 1987.
127. Fortune, S. A sweepline algorithm for Voronoi diagrams, Algorithmica, 2 (1987), 153-174.
128. Fortune, S. Stable maintenance of point-set triangula-Tion in two dimensions, manuscript, AT&T Bell Laboratories. Abbreviated version appeared in: Proc. 30th Ann. Symp. Foundat. Comput. Sci. (1989), 494-499.
129. Fortune, S. Numerical stability of algorithms for 2-d Delaunay triangulations and Voronoi diagrams, Proc. 8th Ann. ACM Symp. Comput. Geom. (1992), 83-92.
130. Fortune, S. Voronoi diagrams and Delaunay triangulations, in: Computing in Euclidean Geometry, eds: D.-Z. Du, F. Hwang, 1, World Scientific (1992), 193-233.
131. Fortune, S. Computational Geometry, ed. R. Martin, Directions in Computational Geometry, Information Geometers, to appear.
132. Fortune, S., Milenkovic, V. Numerical stability of algorithms for line arrangements, Proc. 7th Ann. Symp. Comput. Geom. (1991), 334-341.
133. Fortune, S., Van Wyk, C. J. Efficient exact arithmetic for computational geometry, Proc. 9th Ann. ACM Symp. Comput. Geom. (1993), 163-172.
134. Fredman, M.L. A lower bound on the complexity of orthogonal range queries, J. ACM, 28 (1981), 696-705.
135. Fredman, M.L. Lower bounds on the complexity of some optimal data structures, SIAM J. Comput., 10 (1981), 1-10.
136. Freedman, M.H. Identifying attractors via homology: A technique for time series classification and recognition, manuscript, 1991.
137. Gartner, B. A subexponential algorithm for abstract optimization problems, Proc. 33rd Ann. IEEE Symp. Foundat. Comput. Sci. (1992), 464-472.
138. Garey, M.R., Johnson, D.S., Preparata, F.P., Tarjan, R.E. Triangulating a simple polygon, Inform. Process. Lett., 7 (1978), 175-180.
139. Glassner, A.S. Ray Tracing, Academic Press, 1989.
140. Goodman, J.E., Pollack, R. Multidimensional sorting, SIAM J. Comput., 12 (1983), 484-507.
141. Goodman, J.E., Pollack, R. Upper bounds for configurations and polytopes in R", Disc. Comput. Geom., 1 (1986), 219-227.
142. Goodman, J.E., Pollack, R., Sturmfels, B. The intrinsic spread of a configuration is Sid, J. Amer. Math. Soc., 3 (1990), 639-651.
143. Goodman, J.E., Pollack, R., Wenger, R. Geometric transversal theory, in: New Trends in Discrete and Computational Geometry, ed. J. Pach, Algorithms and Combinatorics, 10, Springer-Verlag (1993), 163-198.
144. Goodrich, M.T. Planar separators and parallel polygon triangulation, Proc. 24th Ann. ACM Symp. Theory Comput. (1992), 507-516.
145. Goodrich, M. T. Constructing arrangements optimally in parallel, Disc. Comput. Geom., 9 (1993), 371-385.
146. Goodrich, M. T., Atallah, M. J., Overmars, M. H. Output-sensitive methods for rectilinear hidden surface removal, Inform. Comput., 107 (1993), 1-24.
147. Goodrich, M.T., Tamassia, R. Dynamic trees and dynamic point location, Proc. 23rd Ann. ACM Symp. Theory Comput. (1991), 523-533.
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.
149. Graham, R.L. An efficient algorithm for determining the convex hull of a planar point set, Inform. Process. Lett., 1 (1972), 132-133.
150. Greene, D., Yao, F. Finite-resolution computational geometry, Proc. 27th Ann. Symp. Foundat. Comput. Sci. (1986), 143-152.
151. Grigor'ev, D. Complexity of deciding Tarski algebra, J. Symbolic Comput., 5 (1988), 37-64.
152. Grigor'ev, D. and Vorobjov, N. Solving systems of polynomial inequalities in subexponential time, J. Symbolic Comput., 5 (1988), 37-64.
153. Guibas, L.J., Knuth, D.E., Sharir, M. Randomized incremental construction of Delaunay and Voronoi diagrams, Algorithmica, 7 (1992), 381-413.
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.
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.
156. Guibas, L.J., Sharir, M. Combinatorics and algorithms of arrangements, New Trends in Discrete and Computational Geometry, J. Pach, ed., 1993, Springer-Verlag, 9-36.
157. Halperin, D., Sharir, M. New bounds for lower envelopes in three dimensions, with applications to visibility in terrains, Proc. 9th Ann. ACM Symp. Comput. Geom. (1993), 11-18.
158. Halperin, 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.
159. Hart, S., Sharir, M. Nonlinearity of Davenport- Schinzel sequences and of generalized path compression schemes, Combinatorica, 6 (1986), 151-177.
160. Haussler, D., Welzl, E. e-nets and simplex range queries, Disc. Comput. Geom., 2 (1987), 127-151.
161. Heintz, J., Roy, M.-F., Solerno, P. On the complexity of semi-Algebraic sets, Proc. IFIP San Francisco, North- Holland (1989), 293-298.
162. Heintz, J., Roy, M.-F., Solerno, P. Sur la complexite du principe de Tarski-Seidenberg, Bull. Soc. Math. France, 118 (1990), 101-126.
163. Heintz, J., Recio, T., Roy, M.-F. Algorithms in real algebraic geometry and applications to computational geometry, Discrete and Computational Geometry, Di- macs Series 6, AMS-ACM, ed. J.E. Goodman, R. Pollack, W. Steiger (1991), 137-163.
164. Hershberger, J., Suri, S. A pedestrian approach to ray shooting: Shoot a ray, take a walk, Proc. 4th ACM- SIAM Symp. Disc. Alg. (1993), 54-63.
165. Hoffmann, C. Geometric and Solid Modeling, Morgan Kaufmann, 1989.
166. Hoffmann, C., Hopcroft, J., Karasick, M. Towards implementing robust geometric computations, Proc. 4th Ann. Symp. Comput. Geom. (1988), 106-117.
167. Hoffmann, C., Hopcroft, J., Karasick, M. Robust set operations on polyhedral solids, IEEE Comput. Graph. Appl., 9 (1989), 50-59.
168. Hopcroft, J., Wilfong, G. Reducing multiple object motion planning to graph searching, SIAM J. Comput., 15 (1986), 768-785.
169. Huttenlocher, D. P. Three-Dimensional Recognition of Solid Objects from a Two-Dimensional Image, Ph.D. Thesis, MIT, Report TR-1045, 1988.
170. Impagliazzo, R., Zuckerman, D. How to recycle random bits, Proc. 30th Ann. IEEE Symp. Foundat. Comput. Sci. (1989), 248-253.
171. Kalai, G. A subexponential randomized simplex algorithm, Proc. 24th Ann. ACM Symp. Theory Comput., 475-482.
172. Karasick, M., Lieber, D., Nackman, L. Efficient De- launay triangulation using rational arithmetic, ACM Trans. Graphics, 10 (1990), 71-91.
173. Karasick, M. On the representation and manipulation of rigid solids, Ph.D. thesis, McGill U., 1988.
174. Katz, M., Sharir, M. Optimal slope selection via expanders, Proc. 5th Canad. Conf. Comput. Geoili., 139-144.
175. Kirkpatrick, D.G. Optimal search in planar subdivisions, SIAM J. Comput., 12 (1983), 28-35.
176. Kirkpatrick, D.G., Klawe, M.M., Tarjan, R.E. Polygon triangulation in 0(n log log n) time with simple data structures, Disc. Comput. Geom., 7 (1992), 329-346.
177. Kirkpatrick D.G., Seidel R. The ultimate planar convex hull algorithm? SIAM J. Comput., 15 (1986), 287-299.
178. Klein, R. Abstract Voronoi diagrams and their applications, Computational Geometry and its Applications, LNCS 333, Springer-Verlag (1988), 148-157.
179. Li, Z., Milenkovic, V. Constructing strongly convex hulls using exact or rounded arithmetic, Proc. 6th Ann. Symp. Comput. Geom. (1990), 235-243.
180. Lipton, R.J., Tarjan, R.E. Applications of a planar separator theorem, SIAM J. Comput., 9 (1980), 615627.
181. Lo, C.-Y, Matousek, J., Steiger, W. Ham-sandwich cuts in Rd, Proc. 24th Ann. ACM Symp. Theory Comput. (1992), 539-545.
182. Luby, M. A simple parallel algorithm for the maximal independent set problem, Proc. 17th Ann. ACM Symp. Theory Comput. (1985), 1-10.
183. Matousek, J. Construction of e-nets, Disc. Comput. Geom., 5 (1990), 427-448.
184. Matousek, J. Cutting hyperplane arrangements, Disc. Comput. Geom., 6 (1991), 385-406.
185. Matousek, J. Approximations and optimal geometric divide-And-conquer, Proc. 23rd ACM Symp. Theory Comput. (1991), 506-511.
186. Matousek, J. Range searching with efficient hierarchical cuttings, Disc. Comput. Geom., 10 (1993), 157-182.
187. Matousek, J. Efficient partition trees, Disc. Comput. Geom., 8 (1992), 315-334.
188. Matousek, J. Reporting points in halfspaces, Comput. Geom. Theory Appl., 2 (1992), 169-186.
189. Matousek, J. Linear optimization queries, J. Algorithms, 14 (1993), 432-448.
190. Matousek, J. Geometric range searching, Tech. Report B-93-09, Free Univ. Berlin, 1993.
191. Matousek, J., Schwarzkopf, O. A deterministic algorithm for the three-dimensional diameter problem, Proc. 25th Ann. ACM Symp. Theory Comput. (1993), 478-484.
192. Matousek, J., Schwarzkopf, O. On ray shooting in convex polytopes, Disc. Comput. Geom., 10 (1993), 215-232.
193. Matousek, J., Sharir, M., Welzl, E. A subexponential bound for linear programming, Proc. 8th ACM Symp. Comput. Geom. (1992), 1-8. To appear in Algorith-Mich.
194. Matousek, J., Welzl, E., Wernisch, L.
195. Megiddo, N. Combinatorial optimization with rational objective functions, Mathematics of Operations Research, 4 (1979), 414-424.
196. Megiddo, N. Applying parallel computation algorithms in the design of serial algorithms, J. ACM, 30 (1983), 852-865.
197. Megiddo, N. Linear programming in linear time when the dimension is fixed, J. ACM, 31 (1984), 114-127.
198. Mehlhorn, K. Data Structures and Algorithms 3: Multidimensional Searching and Computational Geometry, Springer-Verlag, Heidelberg, Germany, 1984.
199. Mehlhorn, K., Simon, K. Intersecting two polyhedra one of which is convex, Proc. Foundat. Comput. Theory, LNCS 199, Springer-Verlag (1985), 534-542.
200. Mehlhorn, K., Yap, C.K. Constructive Whitney- Graustein theorem, or how to untangle closed planar curves, SIAM J. Comput., 20 (1991), 603-621.
201. Milenkovic, V. Verifiable implementations of geometric algorithms using finite precision arithmetic, Artificial Intelligence, 37 (1988), 377-401.
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.
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.
204. Milenkovic, V. Rounding face lattices in the plane, Abstracts 1st Canad. Conf. Comput. Geom. (1989), 12.
205. Milenkovic, V. Rounding face lattices in d dimensions, Proc. 2nd Canad. Conf. Comput. Geom. (1990), 40-45.
206. Mishra, B. Algorithmic Algebra, Springer-Verlag New York, Inc., 1993.
207. Mitchell, S., Vavasis, S. Quality mesh generation in three dimensions, Proc. 8th Ann. ACM Symp. Comput. Geom. (1992), 212-221.
208. Motwani, R., Naor, J., Naor, M. The probabilistic method yields deterministic parallel algorithms, Proc. 30th Ann. IEEE Symp. Foundat. Comput. Sci. (1989), 8-13.
209. Muller, D.E., Preparata, F.P. Finding the intersection of two convex polyhedra, Theoret. Comput. Sci., 7 (1978), 217-236.
210. Mulmuley, K. A fast planar partition algorithm I, Proc. 29th Ann. IEEE Symp. Foundat. Comput. Sci. (1988), 580-589.
211. Mulmuley, K. On obstructions in relation to a fixed viewpoint, Proc. 30th Ann. IEEE Symp. Foundat. Comput. Sci. (1989), 592-597.
212. Mulmuley, K. On levels in arrangements and Voronoi diagrams, Disc. Comput. Geom., 6 (1990), 307-338.
213. Mulmuley, K. A fast planar partition algorithm II, J. ACM, 38 (1991), 74-103.
214. Mulmuley, K. Hidden surface removal with respect to a moving point, Proc. 23rd Ann. ACM Symp. Theory Comput. (1991), 512-522.
215. Mulmuley, K. Randomized multidimensional search trees: dynamic sampling, Proc. 7th Ann. ACM Symp. Comput. Geom. (1991), 121-131.
216. Mulmuley, K. Randomized multidimensional search trees: lazy balancing and dynamic shuffling, Proc. 32nd IEEE Ann. Symp. Foundat. Comput. Sci. (1991), 180-194.
217. Mulmuley, K. Randomized multidimensional search trees: further results in dynamic sampling, Proc. 32nd IEEE Ann. Symp. Foundat. Comput. Sci. (1991), 216-227.
218. Mulmuley, K. Randomized geometric algorithms and pseudo-random generators, Proc. 33rd Ann. IEEE Symp. Foundat. Comput. Sci. (1992), 90-100.
219. Mulmuley, K. Computational Geometry: An Introduction Through Randomized Algorithms, Prentice-Hall, 1994.
220. Naor, J., Naor, M. Small-bias probability spaces: Efficient constructions and applications, Proc. 22nd Ann. ACM Symp. Theory of Comput. (1990), 213-223.
221. Norton, C.H., Plotkin, S.A., Tardos, E. Using separation algorithms in fixed dimensions, J. Algorithms, 13 (1992), 79-98.
222. O'Rourke, J. Art Gallery Theorems and Algorithms, Oxford Univ. Press, New York, NY (1987).
223. O'Rourke, J. Computational Geometry in C, Cambridge Univ. Press, 1994.
224. Pach, J., Agarwal, P.K. Combinatorial Geometry, John Wiley fc Sons, in press.
225. Pach, J., Steiger, W., Szemeredi, E. An upper bound on the number of planar k-sets, Disc. Comput. Geom., 7 (1992), 109-123.
226. Pellegrini, M. Ray shooting on triangles in 3- dimensional space, Algorithmica, 9 (1993), 471-494.
227. Pellegrini, M. On point location and motion planning among simplices, these proceedings.
228. Pollack, R., Roy, M.-F. On the number of cells defined by a set of polynomials, Compte-Rendus, 316 (1993), 573-577.
229. Preparata, F.P., Hong, S.J. Convex hulls of finite sets of points in two and three dimensions, Comm. ACM, 20 (1977), 87-93.
230. Preparata, F.P, Shamos, M.I. Computational Geometry: An Introduction, Springer-Verlag, New York, 1988.
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.
232. Preparata, F.P., Tamassia, R. Efficient point location in a convex spatial cell-complex, SIAM J. Comput., 21 (1992), 267-280.
233. Prill, D. On approximations and incidence in cylindrical algebraic decompositions, SIAM J. Comput., 15 (1986), 972-993.
234. Raghavan, P. Probabilistic construction of deterministic algorithms: Approximating packing integer programs, J. Comput. System Sci., 37 (1988), 130-143.
235. Ramos, E., Intersection of unit-balls and diameter of a set of points in R.3, manuscript, 1994.
236. Reif, J.H., Sen, S. Optimal randomized parallel algorithms for computational geometry, Algorithmica, 7 (1992), 91-117.
237. Renegar, J. On the computational complexity and geometry of the first order theory of the reals, I, II, III, J. Symbolic Comput., 13 (1992), 255-352.
238. Ruppert, J., Seidel, R. On the difficulty of triangulating three-dimensional non-convex polyhedra, Disc. Comput. Geom., 7 (1992), 227-253.
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.
240. Sarnak, N., Tarjan, R.E. Planar point location using persistent search trees, Comm. ACM, 29 (1986), 669679.
241. Schipper, H. Determining contractibility of curves, Proc. 8th Ann. ACM Symp. Comput. Geom. (1992), 358-367.
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), 298-351.
243. Schwartz, J.T., Sharir, M. Algorithmic motion planning in robotics, in: Algorithms and Complexity, Handbook of Theoretical Computer Science, ed. J. van Leeuwen, Vol. A, Elsevier (1990), 391-430.
244. Seidel, R. A convex hull algorithm optimal for point sets in even dimensions, Univ. British Columbia, tech. Rep. 81-14, 1981.
245. Seidel, R. Constructing higher-dimensional convex hulls at logarithmic cost per face, Proc. 18th Ann. ACM Symp. Theory Comput. (1986), 404-413.
246. Seidel, R. Small-dimensional linear programming and convex hulls made easy, Disc. Comput. Geom., 6 (1991), 423-434.
247. Seidel, R. A simple and fast incremental randomized algorithm for computing trapezoidal decompositions and for triangulating polygons, Comput. Geom. Theory Appl. 1 (1991), 51-64.
248. Seidel, R. Backward analysis of randomized geometric algorithms, New Trends in Discrete and Computational Geometry, J. Pach, ed., 1993, Springer-Verlag, 37-67.
249. Seidel, R. The nature and meaning of perturbations in geometric computing, manuscript, 1994.
250. Shamos, M.I., Hoey, D. Closest-point problems, Proc. 16th Ann. IEEE Symp. Foundat. Comput. Sci. (1975), 151-162.
251. Sharir, M. Almost tight upper bounds for lower envelopes in higher dimensions, Proc. 34th Ann. IEEE Symp. Foundat. Comput. Sci. (1993), 498-507.
252. Sharir, M., Agarwal, P.K. Davenport-Schinzel Sequences and Their Geometric Applications, Cambridge Univ. Press, to appear.
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.
254. Spencer, J.H. Ten Lectures on the Probabilistic Method, CBMS-NSF, SIAM, 1987.
255. Sugihara, K., Iri, M. Construction of the Voronoi diagram for one million generators in single precision arithmetic, First Canad. Conf. Comput. Geom., 1989.
256. Sugihara, K., Iri, M. A solid modeling system free from topological inconsistency, J. Information Processing, Information Processing Society of Japan, 12 (1989), 380-393.
257. Tarjan, R.E., Van Wyk, C.J. An 0(n log log n)-Time algorithm for triangulating a simple polygon, SIAM J. Comput., 17 (1988), 143-178.
258. Tourlakis, G., Mylopoulos, J. Some results in computational topology, J. ACM, 20 (1973), 439-455.
259. Vaidya, P.M., Space-Time tradeoffs for orthogonal range queries, SIAM J. Comput., 18 (1989), 748-758.
260. Vapnik, V.N., Chervonenkis, A. Ya. On the uniform convergence of relative frequencies of events to their probabilities, Theory Probab. Appl., 16 (1971), 264280.
261. Vegter, G. Kink-free deformations of polygons, Proc. 5th Ann. ACM Symp. Comput. Geom. (1989), 61-68.
262. Vegter, G., Yap, C.K. Computational complexity of combinatorial surfaces, Proc. 6th Ann. ACM Symp. Comput. Geom. (1990), 102-111.
263. Weispfenning, V. The complexity of linear problems in fields, J. Symbolic Comput., 5 (1988), 3-27.
264. Welzl, E. Partition trees for triangle counting and other range searching problems, Proc. 4th Ann. ACM Symp. Comput. Geom. (1988), 23-33.
265. Welzl, E., On spanning trees with low crossing numbers, Tech. Rep. TR B 92-02, Free University, Berlin, 1992.
266. Whitney, H. Elementary structure of real algebraic varieties, Annals of Math., 66 (1957).
267. Willard, D.E. Polygon retrieval, SIAM J. Comput., 11 (1982), 149-165.
268. Yao, A.C. On the complexity of maintaining partial sums, SIAM J. Comput., 14 (1985), 277-288.
269. Yao, A.C. A lower bound to finding convex hulls, J. ACM, 28 (1981), 780-787.
270. Yao, A.C. Lower bounds for algebraic computation trees with integer inputs, Proc. 30th Ann. IEEE Symp. Foundat. Comput. Sci. (1989), 308-313.
271. Yao, F.F. Computational Geometry, in: Algorithms and Complexity, Handbook of Theoretical Computer Science, ed. J. van Leeuwen, Vol. A, Elsevier (1990), 343-389.
272. Yao, A.C., Yao, F.F. A general approach to d- dimensiond geometric queries, Proc. 17th Ann. ACM Symp. Theory of Comput. (1985), 163-168.
273. Yap, C.K. Symbolic treatment of geometric degeneracies, J. Symbolic Comput., 10 (1990), 349-370.
274. Yap, C.K. A geometric consistency theorem for a symbolic perturbation scheme, J. Comput. Sys. Sci., 40 (1990), 2-18.
275. Yap, C.K. Towards exact geometric computation, Proc. 5th Canad. Conf. Comput. Geom. (1993), 405419.