A randomized polynomial-time simplex algorithm for linear programming

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn 2006, Issue , 2006, Pages 51-60

  Kelner, Jonathan A ^a   Spielman, Daniel A ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b YALE UNIVERSITY   (United States)

Author keywords

Algorithms; Theory

Indexed keywords

ALGORITHMS; PERTURBATION TECHNIQUES; POLYNOMIALS; RANDOM PROCESSES; VECTORS;

BOUNDEDNESS; PERTURBED POLYTOPE; POLYNOMIAL-TIME ALGORITHMS; SHADOW-VERTEX SIMPLEX METHOD;

LINEAR PROGRAMMING;

EID: 33748111098     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1132516.1132524     Document Type: Conference Paper

References (15)

1. D. Bertsimas and S. Vempala. Solving convex programs by random walks. J. ACM, 51(4):540-556, 2004.
2. K. H. Borgwardt. The Simplex Method: a probabilistic analysis. Number 1 in Algorithms and Combinatorics. Springer-Verlag, 1980.
3. G. B. Dantzig. Maximization of linear function of variables subject to linear inequalities. In T. C. Koopmans, editor, Activity Analysis of Production and Allocation, pages 339-347. 1951.
4. G. B. Dantzig. Linear Programming and Extensions. Princeton University Press, 1963.
5. A. Deshpande and D. A. Spielman. Improved smoothed analysis of the shadow vertex simplex method, preliminary version appeared in FOCS '05, 2005.
6. J. Dunagan and S. Vempala. A simple polynomial-time rescaling algorithm for solving linear programs. In Proceedings of the thirty-sixth annual ACM Symposium on Theory of Computing (STOC-04), pages 315-320, New York, June 13-15 2004. ACM Press.
7. K. Fukuda and T. Terlaky. Criss-cross methods: A fresh view on pivot algorithms. Mathematical Programming, 79:369-395, 1997.
8. S. Gass and T. Saaty. The computational algorithm for the parametric objective function. Naval Research Logistics Quarterly, 2:39-45, 1955.
9. M. Grotschel, L. Lovasz, and A. Schrijver. Geometric Algorithms and Combinatorial Optimization, Springer-Verlag, 1991.
10. G. Kalai and D. J. Kleitman. A quasi-polynomial bound for the diameter of graphs of polyhedra. Bulletin Amer. Math. Soc., 26:315-316, 1992.
11. N. Karmarkar. A new polynomial time algorithm for linear programming. Combinatorica, 4:373-395, 1984.
12. L. G. Khachiyan. A polynomial algorithm in linear programming. Doklady Akademia Nauk SSSR, pages 1093-1096, 1979.
13. N. Megiddo and R. Chandrasekaran. On the epsilon-perturbation method for avoiding degeneracy. Operations Research Letters, 8:305-308, 1989.
14. A. Schryver. Theory of Linear and Integer Programming. John Wiley & Sons, 1986.
15. D. A. Spielman and S.-H. Teng. Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time. JACM: Journal of the ACM, 51:385-463, 2004.