A subexponential randomized simplex algorithm

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn Part F129722, Issue , 1992, Pages 475-482

  Kaki, Gil ^a  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; LINEAR PROGRAMMING; COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; RANDOM PROCESSES;

ARITHMETIC OPERATIONS; LINEAR PROGRAMMING PROBLEM; SIMPLEX ALGORITHM;

C (PROGRAMMING LANGUAGE); ALGORITHMS;

SIMPLEX ALGORITHM; SUBEXPONENTIAL RANDOMIZED ALGORITHMS;

EID: 0026972896     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/129712.129759     Document Type: Conference Paper

References (31)

1. A. Björner, M. Las Vergnas, B. Sturmfels, N. White and G. M. Ziegler, Oriented Matroids, Cambridge University Press, 1992, to appear.
2. R. G. Bland, New finite pivoting rules for the simplex method, Math, of Op. Res. 2(1977), 103107.
3. K. H. Borgwardt, The Simplex Method, a Probabilistic Analysis, Algorithms and Combinatorics 1, Springer-Verlag, Berlin, 1987.
4. V. Chvátal, Linear Programming, W. H. Freeman, San Francisco, 1983.
5. K. L. Clarkson, Linear programming in 0(nZd') time, Inform. Process. Lett. 22 (1986), 21-24.
6. K. L. Clarkson, A las Vegas Algorithm for linear programming when the dimension is small, Proceedings STOC 1988, 452-456.
7. G. B. Dantzig, Maximization of a linear function of variables subject to linear inequalities, in: Activity Analysis of Production and Allocation, T. C. Koopman (Ed.) Cowles Commission Monograph 13, Wiley, New York, 1951, 339-347.
8. G. B. Dantzig, Linear Programming and Extensions, Princeton University Press, Princeton, N.J., 1963.
9. M. E. Dyer, On a multidimensional search technique and its application to the Euclidean one-center problem, SIAM J. Comput 15 (1986), 725-738.
10. M. E. Dyer and A. Frieze, random walks, totally unimodular matrices and a randomized dual simplex algorithm, 1992, to appear.
11. D. Gale, How to solve linear inequalities, Amer. Math. Monthly 76(1969),589-599.
12. J. E. Goodman and R. Pollack, Upper bounds for configurations and points in Rd, Discrete and Comp. Geometry, 1(1986), 219-227.
13. B. Grunbaum, Convex Polytopes Ch. 16, Wiley Interscience, London, 1967.
14. G. Kalai, The diameter problem for convex poly-topes and f-vector theory, in: The Victor Klee Festschrift (P. Gritzman and B. Sturmfels, eds.), pp. 387-411, Amer. Math. Society, Providence, 1991.
15. G. Kalai, Upper bounds for the diameter of graphs of convex polytopes, Discrete Comp. Geometry 7(1992), to appear.
16. G. Kalai and D. J. Kleitman, A quasi-polynomial bound for diameter of graphs of polyhedra, Bull. Amer. Math Soc, 24 (Apr. 1992), in press.
17. N. Karmarkar, A new polynomial time algorithm for linear programming, Combinatorica, 4 (1984), 373-397.
18. L. G. Khachiyan, A polynomial algorithm in linear programming, Soviet Math. Doklady, 20 (1979), 191-194.
19. V. Klee, Convex polyhedra and mathematical programming, Proc. 1974 Int. Congress math. Vancouver, 51-56.
20. V. Klee and P. Kleinschmidt, The (d-steps conjecture and its relatives, Math, of Oper. Res. 12(1987), 718-755.
21. V. Klee and G.J. Minty, How good is the simplex algorithm, in: Inequalities III, pp., O. Shisha (ed.) Academic Press, New-York ,1972, pp. 159-175.
22. V. Klee and D. Walkup, The rf-step conjecture for polyhedra of dimension d 6, Acta Math., 133, 53-78.
23. D. G. Larman, Paths on polytopes, Proc. Lon. Math. Soc. 20 (1970), 161-178
24. J. Matoušek, M. Sharir and E. Welzl, A subex-ponential bound for linear programming. V 8-th Annual Symp. on Computetional Geomt. 1992, to appear.
25. P. McMullen, The maximal number of faces of a convex polytope, Mathematika 17(1970), 179184.
26. N. Megiddo, Toward a genuinely polynomial algorithm for linear programming, SIAM J. Comp. 12(1983), 347-353.
27. N. Megiddo, Linear programming in linear time when the dimension is fixed, J. Assoc. Vow Mach. 31(1984), 114-127.
28. A. Schrijver, Theory of Linear and Integer Programming, Wiley-Interscience 1986.
29. R. Seidel, Linear programming and convex hulls made easy, in "Proc. 6th Annual ACM Symposium on Computational Geometry" (1990), 211215.
30. M. Sharir and E. Welzl, A Combinatorial bound for linear programming and related problems, Proc. 9-th Symp. Theor. Aspects of Computer Science (1992), Lecture Notes in Comp. Sci. 577, pp. 569-579, to appear.
31. E. Tardos, A strongly polynomial algorithm to solve combinatorial linear programs, Oper. Res., 34(1986), 250-256.