The Random-Facet Simplex Algorithm on Combinatorial Cubes

Random Structures and Algorithms

Volumn 20, Issue 3, 2002, Pages 353-381

  Gärtner, Bernd ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242330688     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/rsa.10034     Document Type: Conference Paper

References (23)

1. N. Amenta and G. M. Ziegler, Deformed products and maximal shadows, Advances in discrete and computational geometry, J. Chazelle, J. B. Goodman, and R. Pollack (Editors), Contemporary Mathematics, Am. Math. Soc., Providence, RI, 57-90, 1998.
2. A. Z. Broder, M. E. Dyer, A. M. Frieze, P. Raghavan, and E. Upfal, The worst-case running time of the random simplex algorithm is exponential in the height, Inform Proc Lett 56(2) (1995), 79-81.
3. V. Chvátal, Linear programming, W. H. Freeman, New York, 1983.
4. G. B. Dantzig, Linear programming and extensions, Princeton University Press, Princeton, NJ, 1963.
5. L. Finschi, K. Fukuda, and H.-J. Lüthi. Towards a unified framework for randomized pivoting algorithms in linear programming, Operations Research Proceedings, Springer-Verlag, New York, 1998, pp. 113-122.
6. B. Gärtner, Randomized optimization by simplex-type methods, Ph.D. thesis, Freie Universität Berlin, 1995.
7. B. Gärtner, Combinatorial linear programming: Geometry can help, Proc Second Workshop Randomization and Approximation Techniques in Computer Science (RANDOM'98), Lecture Notes in Computer Science, 1518 Springer-Verlag, New York, 1998, pp. 82-96.
8. B. Gärtner, M. Henk, and G. M. Ziegler, Randomized simplex algorithms on Klee-Minty cubes, Combinatorica 18(3) (1998), 349-372.
9. B. Gärtner and V. Kaibel, Abstract objective function graphs on the 3-cube - a characterization by readability, Technical Report TR 296, Department of Computer Science, ETH, Zürich, 1998.
10. B. Gärtner, J. Solymosi, F. Tschirschnitz, P. Valtr, and E. Welzl, One line and n points, Proc 33rd Annu ACM Symp Theory of Computing (STOC), 2001, to appear.
11. M. Goldwasser, A survey of linear programming in randomized subexponential time, ACM-SIGACT News 26(2) (1995), 96-104.
12. K. Williamson Hoke, Completely unimodal numberings of a simple polytope, Discrete Appl Math 20 (1988), 69-81.
13. F. Holt and V. Klee, A proof of the strict monotone 4-step conjecture. Advances in discrete and computational geometry, J. Chazelle, J.B. Goodman, and R. Pollack (Editors), Contemporary Mathematics, Am. Math. Soc., Providence, RI, 201-216, 1998.
14. R. G. Jeroslow, The simplex algorithm with the pivot rule of maximizing criterion improvement, Discrete Math 4 (1973), 367-377.
15. M. Joswig and V. Kaibel, Randomized simplex algorithms and random cubes, manuscript.
16. G. Kalai, A subexponential randomized simplex algorithm, Proc 24th Annu ACM Symp Theory of Computing, 1992, pp. 475-482.
17. G. Kalai, Linear programming, the simplex algorithm and simple polytopes, Math Program 79 (1997), 217-233.
18. V. Klee and G. J. Minty, How good is the simplex algorithm? Inequalities III, O. Shisha (Editor), Academic Press, New York, 1972, pp. 159-175.
19. J. Matoušek, Lower bounds for a subexponential optimization algorithm, Random Struct Alg 5(4) (1994), 591-607.
20. J. Matoušek, M. Sharir, and E. Welzl, A subexponential bound for linear programming, Algorithmica 16 (1996), 498-516.
21. J. Mihalisin and V. Klee, Convex and linear orientations of polytopal graphs, Discrete Comput Geom 24 (2000), 421-436.
22. N. Zadeh, What is the worst case behavior of the simplex algorithm?, Technical Report 27, Department of Operations Research, Stanford University, Stanford, CA, 1980.
23. G. M. Ziegler, Lectures on polytopes, Graduate Texts in Mathematics 152, Springer-Verlag, New York, 1994.