Lectures on discrete geometry
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[1] J. Steiner. Einige Gesetze über die Theilung der Ebene und des Raumes. , 1826 .
[2] L. Schläfli. Theorie der vielfachen Kontinuität , 1901 .
[3] Georges Voronoi. Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Deuxième mémoire. Recherches sur les parallélloèdres primitifs. , 1908 .
[4] J. Radon. Mengen konvexer Körper, die einen gemeinsamen Punkt enthalten , 1921 .
[5] P. Vincensini. Sur une extension d'un théorème de M. J. Radon sur les ensembles de corps convexes , 1939 .
[6] R. Rado. A Theorem on General Measure , 1946 .
[7] V. Klee. The Critical Set of a Convex Body , 1953 .
[8] V. Klee,et al. The generation of convex hulls , 1963 .
[9] V. Klee. On the Number of Vertices of a Convex Polytope , 1964, Canadian Journal of Mathematics.
[10] J. Milnor. On the Betti numbers of real varieties , 1964 .
[11] P. McMullen. The maximum numbers of faces of a convex polytope , 1970 .
[12] G. C. Shephard,et al. Convex Polytopes and the Upper Bound Conjecture , 1971 .
[13] B. Grünbaum. Arrangements and Spreads , 1972 .
[14] G. T. Sallee. A helly-type theorem for widths , 1975 .
[15] T. Zaslavsky. Facing Up to Arrangements: Face-Count Formulas for Partitions of Space by Hyperplanes , 1975 .
[16] M. Katchalski. A Helly type Theorem for Convex Sets , 1978, Canadian Mathematical Bulletin.
[17] E. Buchman,et al. Any New Helly Numbers , 1982 .
[18] A. Brøndsted. An Introduction to Convex Polytopes , 1982 .
[19] D. T. Lee,et al. On k-Nearest Neighbor Voronoi Diagrams in the Plane , 1982, IEEE Transactions on Computers.
[20] Michael Ben-Or,et al. Lower bounds for algebraic computation trees , 1983, STOC.
[21] Richard Pollack,et al. On the Number of k-Subsets of a Set of n Points in the Plane , 1984, J. Comb. Theory, Ser. A.
[22] Noga Alon,et al. A Simple Proof of the Upper Bound Theorem , 1985, Eur. J. Comb..
[23] Vojtech Rödl,et al. Geometrical realization of set systems and probabilistic communication complexity , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).
[24] Bernard Chazelle,et al. The power of geometric duality , 1985, BIT Comput. Sci. Sect..
[25] Chee-Keng Yap,et al. A "Retraction" Method for Planning the Motion of a Disc , 1985, J. Algorithms.
[26] Richard Pollack,et al. Upper bounds for configurations and polytopes inRd , 1986, Discret. Comput. Geom..
[27] Noga Alon,et al. The number of small semispaces of a finite set of points in the plane , 1986, J. Comb. Theory, Ser. A.
[28] Raimund Seidel,et al. Constructing Arrangements of Lines and Hyperplanes with Applications , 1986, SIAM J. Comput..
[29] N. Alon. The number of polytopes, configurations and real matroids , 1986 .
[30] F. Aurenhammer,et al. Geometric relations among Voronoi diagrams , 1987, STACS.
[31] N. Mnev. The universality theorems on the classification problem of configuration varieties and convex polytopes varieties , 1988 .
[32] Kenneth L. Clarkson,et al. A Randomized Algorithm for Closest-Point Queries , 1988, SIAM J. Comput..
[33] Kenneth L. Clarkson,et al. Applications of random sampling in computational geometry, II , 1988, SCG '88.
[34] Leonidas J. Guibas,et al. A Singly-Expenential Stratification Scheme for Real Semi-Algebraic Varieties and Its Applications , 1989, ICALP.
[35] Rolf Klein,et al. Concrete and Abstract Voronoi Diagrams , 1990, Lecture Notes in Computer Science.
[36] Peter W. Shor,et al. Stretchability of Pseudolines is NP-Hard , 1990, Applied Geometry And Discrete Mathematics.
[37] Bernard Chazelle,et al. A deterministic view of random sampling and its use in geometry , 1990, Comb..
[38] David Eppstein,et al. Horizon Theorems for Lines and Polygons , 1990, Discrete and Computational Geometry.
[39] Leonidas J. Guibas,et al. Combinatorial complexity bounds for arrangements of curves and spheres , 1990, Discret. Comput. Geom..
[40] R. Živaljević,et al. An Extension of the Ham Sandwich Theorem , 1990 .
[41] R. Pollack,et al. The Intrinsic Spread of a Configuration in R d , 1990 .
[42] Franz Aurenhammer,et al. Voronoi diagrams—a survey of a fundamental geometric data structure , 1991, CSUR.
[43] Jean-Claude Latombe,et al. Robot motion planning , 1970, The Kluwer international series in engineering and computer science.
[44] Leonidas J. Guibas,et al. A Singly Exponential Stratification Scheme for Real Semi-Algebraic Varieties and its Applications , 1991, Theor. Comput. Sci..
[45] David Avis,et al. A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra , 1991, SCG '91.
[46] Raimund Seidel,et al. Small-dimensional linear programming and convex hulls made easy , 1991, Discret. Comput. Geom..
[47] Leonidas J. Guibas,et al. Computing a face in an arrangement of line segments , 1991, SODA '91.
[48] P. Orlik,et al. Arrangements Of Hyperplanes , 1992 .
[49] Marie-Françoise Roy,et al. Real algebraic geometry , 1992 .
[50] Atsuyuki Okabe,et al. Spatial Tessellations: Concepts and Applications of Voronoi Diagrams , 1992, Wiley Series in Probability and Mathematical Statistics.
[51] Micha Sharir,et al. On the zone of a surface in a hyperplane arrangement , 1993, Discret. Comput. Geom..
[52] Bernard Chazelle,et al. Cutting hyperplanes for divide-and-conquer , 1993, Discret. Comput. Geom..
[53] R. Pollack,et al. On the number of cells defined by a set of polynomials , 1993 .
[54] William L. Steiger,et al. Algorithms for ham-sandwich cuts , 1994, CCCG.
[55] Micha Sharir,et al. On the Zone Theorem for Hyperplane Arrangements , 1991, SIAM J. Comput..
[56] Bernard Chazelle,et al. An optimal convex hull algorithm in any fixed dimension , 1993, Discret. Comput. Geom..
[57] M. Sharir,et al. On the sum of squares of cell complexities in hyperplane arrangements , 1994 .
[58] Asish Mukhopadhyay,et al. Computing a centerpoint of a finite planar set of points in linear time , 1994, Discret. Comput. Geom..
[59] G. Ziegler. Lectures on Polytopes , 1994 .
[60] Ketan Mulmuley,et al. Computational geometry : an introduction through randomized algorithms , 1993 .
[61] R. Pollack,et al. Arrangements and Topological Planes , 1994 .
[62] David Eppstein,et al. Dynamic Euclidean minimum spanning trees and extrema of binary functions , 1995, Discret. Comput. Geom..
[63] R. Graham,et al. Handbook of Combinatorics , 1995 .
[64] David Eppstein,et al. Approximating center points with iterative Radon points , 1996, Int. J. Comput. Geom. Appl..
[65] S. Basu,et al. On the number of cells defined by a family of polynomials on a variety , 1996 .
[66] Jürgen Richter-Gebert. Realization Spaces of Polytopes , 1996 .
[67] J. Matousek,et al. On the distortion required for embedding finite metric spaces into normed spaces , 1996 .
[68] Joseph O'Rourke,et al. Handbook of Discrete and Computational Geometry, Second Edition , 1997 .
[69] Raimund Seidel,et al. How Good Are Convex Hull Algorithms? , 1997, Comput. Geom..
[70] Raimund Seidel. Convex hull computations , 1997 .
[71] Stefan Felsner. On the Number of Arrangements of Pseudolines , 1997, Discret. Comput. Geom..
[72] Jean-Paul Laumond,et al. Algorithms for Robotic Motion and Manipulation , 1997 .
[73] David A. Cox,et al. Ideals, Varieties, and Algorithms , 1997 .
[74] Mark de Berg,et al. Computational geometry: algorithms and applications , 1997 .
[75] Jirí Matousek,et al. Computing Many Faces in Arrangements of Lines and Segments , 1998, SIAM J. Comput..
[76] Bernard Chazelle,et al. The Discrepancy Method , 1998, ISAAC.
[77] Alexander Schrijver,et al. Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.
[78] Bernard Chazelle,et al. Product range spaces, sensitive sampling, and derandomization , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.
[79] Michael Joswig,et al. polymake: a Framework for Analyzing Convex Polytopes , 2000 .
[80] Timothy M. Chan. Random Sampling, Halfspace Range Reporting, and Construction of (<= k)-Levels in Three Dimensions , 2000, SIAM J. Comput..
[81] Micha Sharir,et al. Arrangements and Their Applications , 2000, Handbook of Computational Geometry.
[82] G. Ziegler,et al. Polytopes : combinatorics and computation , 2000 .
[83] J. Sack,et al. Handbook of computational geometry , 2000 .
[84] Micha Sharir,et al. The Clarkson-Shor technique revisited and extended , 2001, SCG '01.
[85] Emo Welzl,et al. Entering and leaving j-facets , 2001, Discret. Comput. Geom..
[86] Vladlen Koltun,et al. Almost tight upper bounds for vertical decompositions in four dimensions , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.
[87] Murali K. Ganapathy,et al. On the number of zero-patterns of a sequence of polynomials , 2001 .
[88] Boris Aronov,et al. A lower bound on Voronoi diagram complexity , 2002, Inf. Process. Lett..
[89] Marc E. Pfetsch,et al. Computing the face lattice of a polytope from its vertex-facet incidences , 2002, Comput. Geom..
[90] G. Ziegler,et al. Fat 4-polytopes and fatter 3-spheres , 2002, math/0204007.
[91] Timothy M. Chan. On Levels in Arrangements of Curves , 2003, Discret. Comput. Geom..
[92] S. Basu,et al. Algorithms in real algebraic geometry , 2003 .
[93] Jacob E. Goodman. Pseudoline Arrangements , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..