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On linear-time deterministic algorithms for optimization problems in fixed dimension

Published: 01 January 1993 Publication History
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References

[1]
B. Berger and J. Rompel. Simulating (log n)C-wise independence in NC. Journal of the ACM, 38(4):1028- 1046, 1991.
[2]
B. Berger, J. Rompel, and P. W. Shor. Efficient N C algorithms for set cover with applications to learning and geometry. In Proc. 30. IEEE Symposium on Foundations of Computer Science, pages 54-59, 1989.
[3]
B. Chazelle and J. Friedman. A deterministic view of random sampling and its use in geometry. Combinatorica, 10(3):229-249, 1990.
[4]
B. Chazelle. Cutting hyperplanes for divide-andconquer. Tech. report CS-TR-335-91, Princeton University, 1991. Preliminary version: Proc. 32. IEEE Symposium on Foundations of Computer Science, 29- 38, October 1991.
[5]
K. Clarkson. Linear programming in O(nx3d2) time. In.formation Processing Letters, 22(1):21-24, 1986.
[6]
K. Clarkson. Las Vegas algorithm for linear programming when the dimension is small. In Proc. 29. IEEE Symposium on Foundations of Computer Science, pages 452-457, 1988.
[7]
M. E. Dyer and A. M. Frieze. A randomized algorithm for fixed-dimensional linear programming. Manuscript, 1987.
[8]
L. Danzer, D. Laugwitz, and H. Lenz. Uber das LSwnersche Ellipsoid und seine Anlagen unter den einem EikSrper einbeschriebenen Ellipsoid. Archiv der Mathematik, 8:214-219, 1957.
[9]
E. M. Dyer. On a multidimensional search technique and its application to the Euclidean 1-centre problem. SiAM Journal on Computing, 15:725-738, 1986.
[10]
M. E. Dyer. A dass of convex programs with applications to computational geometry. In Proc. 8. A CM Symposium on Computational Geometry, pages 9-15, 1992.
[11]
B. Gilrtner. Abstract optimization problems. In Proc. 33. IEEE Symposium on Foundations of Computer Science, 1992. To appear.
[12]
D. Haussler and E. Welzl. e-nets and simplex range queries. Discrete ~ Computational Geometry, 2:127- 151, 1987.
[13]
F. Juhnke. Volumenminimale Ellipsoidiiberdeckungen. Beitrdige zur Algebra und Geometrie, 30:143-153, 1990.
[14]
G. KaJai. A subexponential randomized simplex algorithm. In Proc. ~~. A CM Symposium on Theory of Computing, 1992.
[15]
N. Karmakar. A new polynomial-time algorithm for linear programming. Combinatorica, 4:373-395, 1984.
[16]
L. G. Khachiyan. Polynomial Mgorithm in linear programming. U.S.S.R. Comput. Math. and Math. Phys., 20:53-72, 1980.
[17]
J. Koml6s, J. Pach, and G. WSginger. Almost tight bounds for epsilon-nets. Discrete f.4 Computational Geometry, 1992. To appear.
[18]
J. Matou.%k. Approximations and optimal geometric divide-and-conquer. In Proc. ~3. A CM Symposium on Theory of Computing, pages 506-511, 1991.
[19]
N. Megiddo. Linear programming in linear time when the dimension is fixed. Journal of the A CM, 31:114-127, 1984.
[20]
R. Motwani, J. Naor, and M. Naor. The probabilistic method yields deterministic parallel algorithms. In Proc. 30th Annu. IEEE Sympos. Found. Comput. Sci., pages 8-13, 1989.
[21]
J. Matouiek, M. Sharir, and E. Welzl. A subexponential bound for linear programming. In Proc. 8. A CM Symposium on Computational Geometry, pages 1-8, 1992.
[22]
J. Matouiek, E. Welzl, and L. Wernisch. Discrepancy and e-approximations for bounded VC-dimension. Combinatorica, 1992. To appear; also in Proc. 32. IEEE Symposium on Foundations of Computer Science (1991), pages 424-430.
[23]
M. J. Post. Minimum spanning ellipsoids. In Proc. 16. A CM Symposium on Theory of Computing, pages 108-116, 1984.
[24]
J. Renegar. On the computational complexity and geometry of the first order theory of the reals. Journal of Symbolic Computation, 1992.
[25]
N. Sauer. On the density of families of sets. Journal of Combinatorial Theory Set. A, 13:145-147, 1972.
[26]
R. Seidel. Small dimensional linear programming and convex hulls made easy. Discrete f_4 Computational Geometry, 6(5):423-434, 1991.
[27]
J. Spencer. Ten lectures on the probabilistic method. CBMS-NSF, SIAM, 1987.
[28]
M. Sharir and E. Welzl. A combinatorial bound for linear programming and related problems. In Proc. 1992 Symposium on Theoretical Aspects of Computer Science (Lecture Notes in Computer Science), volume 577, pages 569-579. Springer-Verlag, 1992.
[29]
V. N. Vapnik and A. Ya. Chervonenkis. On the uniform convergence of relative frequencies of events to their probabilities. Theory Probab. Appl., 16:264-280, 1971.
[30]
E. Welzl. SmMlest enclosing disks (balls and ellipsoids). In H. Maurer, editor, LNCS 555 (New Results and New Trends in Computer Science), pages 359-370. Springer-Verlag, 1991.
[31]
E. Welzl. New results on linear programming and related problems (survey paper). Manuscript, 1992.
[32]
F. F. Yao and A. C. Yao. A general approach to geometric queries. In Proc. 17. A CM Symposium on Theory of Computing, pages 163-168, 1985.

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cover image ACM Conferences
SODA '93: Proceedings of the fourth annual ACM-SIAM symposium on Discrete algorithms
January 1993
506 pages
ISBN:0898713137

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Society for Industrial and Applied Mathematics

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Published: 01 January 1993

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SODA93: Conference on Discrete Algorithms
January 25 - 27, 1993
Texas, Austin, USA

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Overall Acceptance Rate 411 of 1,322 submissions, 31%

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