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Abstract: We survey techniques for replacing randomized algorithms in computational geometry by deterministic ones with a similar asymptotic running time. 1 Randomized algorithms and derandomization A rapid growth of knowledge about randomized algorithms stimulates research in derandomization, that is, replacing randomized algorithms by deterministic ones with as small decrease of efficiency as possible. Related to the problem of derandomization is the question of reducing the amount of random bits... (Update)
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BibTeX entry: (Update)
J. Matousek. Derandomization in computational geometry. Journal of Algorithms 20 (1996), 545--580. http://citeseer.ist.psu.edu/matousek96derandomization.html More
@article{ matousek96derandomization,
author = "Jiri Matousek",
title = "Derandomization in Computational Geometry",
journal = "J. Algorithms",
volume = "20",
number = "3",
pages = "545-580",
year = "1996",
url = "citeseer.ist.psu.edu/matousek96derandomization.html" }
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218 Probabilistic construction of deterministic algorithms: appr.. (context) - Raghavan - 1988
214 Davenport-Schinzel Sequences and Their Geometric Application.. - Sharir, Agarwal - 1995
186 Computational Geometry: An Introduction Through Randomized A.. (context) - Mulmuley - 1994
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133 Geometric range searching and its relatives - Agarwal, Erickson - 1997
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122 Linear programming in linear time when the dimension is fixe.. (context) - Megiddo - 1984
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108 Combinatorial complexity bounds for arrangements of curves a.. (context) - Clarkson, Edelsbrunner et al. - 1990
98 volume 10 of EATCS Monographs on Theoretical Computer Scienc.. (context) - Edelsbrunner, Combinatorial - 1987
91 Epsilon-nets and simplex range queries (context) - Haussler, Welzl - 1987
90 New applications of random sampling in computational geometr.. - Clarkson - 1987
87 Applications of parametric searching in geometric optimizati.. - Agarwal, Sharir et al. - 1992
81 A subexponential bound for linear programming - Matousek, Sharir et al. - 1996
81 On range searching with semialgebraic sets - Agarwal, Matousek - 1994
80 Slowing down sorting networks to obtain faster sorting algor.. (context) - Cole - 1987
79 Cutting hyperplanes for divide-and-conquer (context) - Chazelle - 1993
75 A deterministic view of random sampling and its use in geome.. (context) - Chazelle, Friedman - 1990
72 Efficient partition trees (context) - Matousek - 1992
69 A fast planar partition algorithm (context) - Mulmuley - 1991
69 A fast planar partition algorithm (context) - Mulmuley - 1990
69 Small-dimensional linear programming and convex hulls made e.. (context) - Seidel - 1991
65 Combinatorial optimization with rational objective functions (context) - Megiddo - 1979
64 A randomized algorithm for closest-point queries (context) - Clarkson - 1988
61 Expanders that beat the eigenvalue bound: Explicit construct.. - Wigderson, Zuckerman - 1993
58 Reporting points in halfspaces (context) - Matousek - 1992
56 Constructing higher-dimensional convex hulls at logarithmic .. (context) - Seidel - 1986
55 Backwards analysis of randomized geometric algorithms - Seidel - 1993
53 The probabilistic method yields deterministic parallel algor.. - Motwani, Naor et al. - 1994
51 Almost optimal set covers in finite VC-dimension (context) - Bronnimann, Goodrich - 1995
50 On linear-time deterministic algorithms for optimization pro.. - Chazelle, Matousek - 1996
49 A simple and fast incremental randomized algorithm for compu.. - Seidel - 1991
48 Las Vegas algorithms for linear and integer programming - Clarkson - 1995
47 hulls and related problems (context) - Cole, Sharir et al. - 1987
43 Approximations and optimal geometric divide-and-conquer (context) - Matousek - 1995
43 An optimal convex hull algorithm in any fixed dimension (context) - Chazelle - 1993
43 A subexponential randomized simplex algorithm (context) - Kalai - 1992
42 Parallel algorithms for higherdimensional convex hulls - Amato, Goodrich et al. - 1994
42 wise independence in NC (context) - Berger, Rompel et al. - 1991
42 An optimal-time algorithm for slope selection (context) - Cole, Salowe et al. - 1989
41 Randomized optimal algorithm for slope selection (context) - Matousek - 1991
41 Removing randomness in parallel computation without processo.. - Luby - 1993
40 Approximations of general independent distributions - Even, Goldreich et al. - 1992
40 Geometric range searching - Matousek - 1995
39 An expander-based approach to geometric optimization (context) - Katz, Sharir - 1993
38 On lazy randomized incremental construction - de Berg, Dobrindt et al. - 1995
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37 Irregularities of Distribution (context) - Beck, Chen - 1987
36 A general approach to D-dimensional geometric queries (context) - Yao, Yao - 1985
36 On ray shooting in convex polytopes (context) - Matousek, Schwarzkopf - 1993
36 A singly-exponential stratification scheme for real semi-alg.. (context) - Chazelle, Edelsbrunner et al. - 1989
34 A randomized algorithm for slope selection (context) - Dillencourt, Mount et al. - 1992
31 Cutting hyperplane arrangements (context) - Matousek - 1991
30 Selecting distances in the plane (context) - Agarwal, Aronov et al. - 1990
30 Wiley and Sons (context) - Alon, Spencer et al. - 1993
29 Linear optimization queries - Matousek - 1993
29 An optimal algorithm for finding segment intersections (context) - Balaban - 1995
28 Quasi-optimal range searching in spaces of finite VC-dimensi.. (context) - Chazelle, Welzl - 1989
28 randomized construction of small sample spaces in NC - Karger, Koller - 1994
28 Geometric partitioning made easier (context) - Goodrich - 1993
27 Fixed-dimensional linear programming queries made easy - Chan - 1996
27 Strongly polynomial-time and NC algorithms for detecting cyc.. (context) - Cohen, Megiddo - 1993
27 Building Voronoi diagrams for convex polygons in linear expe.. (context) - Chew - 1986
26 closest line pair and parametric searching (context) - Chazelle, Edelsbrunner et al. - 1993
25 Optimal slope selection via cuttings (context) - Bronnimann, Chazelle - 1994
24 Derandomizing an output-sensitive convex hull algorithm in t.. (context) - Chazelle, Matousek - 1994
24 Computing many faces in arrangements of lines and segments - Agarwal, Matousek et al. - 1994
24 Algebraic Geometry (context) - Harris - 1992
23 Product range spaces (context) - Bronnimann, Chazelle et al. - 1993
23 Optimal slope selection via expanders - Katz, Sharir - 1993
22 A deterministic algorithm for the three-dimensional diameter.. - Matousek, Schwarzkopf - 1996
21 Polygon retrieval (context) - Willard - 1982
21 Computing a face in an arrangement of line segments and rela.. (context) - Chazelle, Edelsbrunner et al. - 1993
21 Red-blue intersection detection algorithms (context) - Agarwal, Sharir - 1990
20 A fast and simple randomized algorithm for the maximal indep.. (context) - Alon, Babai et al. - 1986
20 Randomized geometric algorithms - Clarkson - 1992
20 Efficient NC algorithms for set cover with applications to l.. (context) - Berger, Rompel et al. - 1994
19 Using separation algorithms in fixed dimensions - Norton, Plotkin et al. - 1992
19 Algorithms for ham-sandwich cuts (context) - Lo, Matousek et al. - 1994
18 A class of convex programs with applications to computationa.. (context) - Dyer - 1992
17 On levels in arrangements and Voronoi diagrams (context) - Mulmuley - 1991
17 An introduction to randomized algorithms (context) - Karp - 1991
17 Algorithms for diametral pairs and convex hulls that are opt.. (context) - Clarkson, Shor - 1988
16 Lines in space: combinatorics (context) - Chazelle, Edelsbrunner et al. - 1989
16 Computing faces in segment and simplex arrangements - Amato, Goodrich et al. - 1995
15 Combinatorics and algorithms of arrangements (context) - Guibas, Sharir - 1993
15 Approximating center points with iterated Radon points - Clarkson, Eppstein et al. - 1996
15 lower envelopes and applications (context) - Ramos, -d - 1997
14 Geometric partitioning and its applications (context) - Agarwal - 1991
14 Construction of ffl-nets (context) - Matousek - 1990
14 a combinatorial game (context) - Erdos, Selfridge - 1973
13 approximations for bounded VC-dimension (context) - Matousek, Welzl et al. - 1993
13 wise independent random variables (context) - Karloff, Mansour et al. - 1994
12 Randomized algorithms and pseudorandom numbers (context) - Karloff, Raghavan - 1993
12 Almost tight bounds for ffl-nets (context) - Koml'os, Pach et al. - 1992
11 Parametric combinatorial computing and a problem of program .. (context) - Gusfield - 1983
11 Mathematical techniques for efficient record segmentation in.. (context) - Eisner, Severance - 1976
9 Partitioning and geometric embedding of range spaces of fini.. (context) - Alon, Haussler et al. - 1987
9 Fixed-dimensional parallel linear programming via relative f.. (context) - Goodrich - 1996
9 processor algorithm for linear programming in fixed dimensio.. (context) - Ajtai, Megiddo et al. - 1992
7 On point location and motion planning among simplices - Pellegrini - 1996
7 An efficient multidimensional searching technique and its ap.. - Agarwal, Sharir et al. - 1993
7 A parallel algorithm for linear programming in fixed dimensi.. (context) - Dyer - 1995
7 Randomized geometric algorithms and pseudo-random generators (context) - Mulmuley - 1996
5 Solving some discrepancy problems in NC - Mahajan, Ramos et al. - 1997
5 How to net a lot with little: small ffl-nets for disks and h.. (context) - Matousek, Seidel et al. - 1990
4 An efficient deterministic algorithm (context) - Agarwal, of - 1990
3 Private communication (context) - Ramos - 1996
2 Derandomized algorithms in combinatorial optimization (context) - Srivastav - 1995
2 An algorithm for intersecting equal radius balls in R (context) - Ramos - 1994
2 Available electronically at http://www (context) - Luby, Wigderson et al. - 1995
2 Techniques for computing with low-independence randomness (context) - Rompel - 1990
2 Pseudorandom generators for space-bounded computation (context) - Nissan - 1992
1 Chernoff-Hoeffending bounds for applications with limited in.. (context) - Schmidt, Siegel et al. - 1995
1 A fast parallel algorithm for the maximum independent set pr.. (context) - Karp, Wigderson - 1985
1 Constructin small sample spaces satisfying given constraints (context) - Koller, Megiddo - 1994
1 Max-Planck Institut fur Informatik (context) - Ramos - 1997
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Geometric Set Systems - Matousek (1998) (Correct)
A lower bound for families of Natarajan dimension d - Fischer, Matousek (Correct)
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