Combinatorial linear programming: Geometry can help

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1518, Issue , 1998, Pages 82-96

  Gärtner, Bernd ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

RANDOM PROCESSES; SOFTWARE ARCHITECTURE;

ABSTRACT NOTIONS; CLASS A; COMBINATORIAL LINEAR PROGRAMMING; LINEAR PROGRAMS; SIMPLEX ALGORITHM; SIMPLEX METHODS;

LINEAR PROGRAMMING;

EID: 84958610653     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-49543-6_8     Document Type: Conference Paper

References (21)

1. I. Adler and R. Saigal. Long monotone paths in abstract polytopes. Math. Operations Research, 1(1):89-95, 1976.
2. N. Amenta and G. M. Ziegler. Deformed products and maximal shadows. In J. Chazelle, J.B. Goodman, and R. Pollack, editors, Advances in Discrete and Computational geometry, Contemporary Mathematics. Amer. Math. Soc., 1998.
3. D. Barnette. A short proof of the d-connectedness of d-polytopes. Discrete Math., 137:351-352, 1995
4. R. G. Bland. New nite pivoting rules for the simplex method. Math. Operations Research, 2:103-107, 1977.
5. V. Chvátal. Linear Programming. W. H. Freeman, New York, NY, 1983.
6. G. B. Dantzig. Linear Programming and Extensions. Princeton University Press, Princeton, NJ, 1963.
7. B. Gärtner. Randomized Optimization by Simplex-Type Methods. PhD thesis, Freie Universität Berlin, 1995.
8. B. Gartner. A subexponential algorithm for abstract optimization problems. SIAM J. Comput., 24:1018-1035, 1995.
9. B. Gärtner, M. Henk, and G. M. Ziegler. Randomized simplex algorithms on Klee-Minty cubes. Combinatorica (to appear).
10. B. Gärtner and V. Kaibel. Abstract objective function graphs on the 3-cube - a characterization by realizability. Technical Report TR 296, Dept. of Computer Science, ETH Zürich, 1998.
11. B. Gartner and E. Welzl. Linear programming - randomization and abstract frameworks. In Proc. 13th annu. Symp. on Theoretical Aspects of Computer Science (STACS), volume 1046 of Lecture Notes in Computer Science, pages 669-687. Springer-Verlag, 1996.
12. D. Goldfarb. On the complexity of the simplex algorithm. In S. Gomez, editor, IV. Workshop on Numerical Analysis and Optimization, Oaxaca, Mexico, 1993.
13. K. Williamson Hoke. Completely unimodal numberings of a simple polytope. Discr. Applied Math., 20:69-81, 1988.
14. F. Holt and V. Klee. A proof of the strict monotone 4-step conjecture. In J. Chazelle, J.B. Goodman, and R. Pollack, editors, Advances in Discrete and Computational geometry, Contemporary Mathematics. Amer. Math. Soc., 1998.
15. G. Kalai. A subexponential randomized simplex algorithm. In Proc. 24th annu. ACM Symp. on Theory of Computing., pages 475-482, 1992.
16. G. Kalai. Linear programming, the simplex algorithm and simple polytopes. Math. Programming, 79:217-233, 1997.
17. L. G. Khachiyan. Polynomial algorithms in linear programming. U.S.S.R. Comput. Math. and Math. Phys, 20:53-72, 1980.
18. V. Klee and G. J. Minty. How good is the simplex algorithm? In O. Shisha, editor, Inequalities III, pages 159-175. Academic Press, 1972.
19. J. Matoušek, M. Sharir, and E. Welzl. A subexponential bound for linear programming. Algorithmica, 16:498-516, 1996.
20. J. Matoušek. Lower bounds for a subexponential optimization algorithm. Random Structures & Algorithms, 5(4):591-607, 1994.
21. M. Sharir and E. Welzl. Rectilinear and polygonal p-piercing and p-center problems. In Proc. 12th Annu. ACM Sympos. Comput. Geom., pages 122-132, 1996.