Complexity of linear programming

Authors:
J. F. Traub;H. Woniakowski
Affiliations:
Department of Computer Science, Columbia University, New York, NY 10027, U.S.A.;Institute of Informatics, University of Warsaw, Warsaw, Poland and Department of Computer Science, Columbia University, New York, NY 10027, U.S.A.
Venue:
Operations Research Letters
Year:
1982

Citing 2
Cited 1

Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems

Journal of the ACM (JACM)
The Design and Analysis of Computer Algorithms

The Design and Analysis of Computer Algorithms

On the probabilistic complexity of finding an approximate solution for linear programming

Journal of Complexity

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Abstract

The complexity of linear programming is discussed in the ''integer'' and ''real number'' models of computation. Even though the integer model is widely used in theoretical computer science, the real number model is more useful for estimating an algorithm's running time in actual computation. Although the ellipsoid algorithm is a polynomial-time algorithm in the integer model, we prove that it has unbounded complexity in the real number model. We conjecture that there exists no polynomial-time algorithm for the linear inequalities problem in the real number model. We also conjecture that linear inequalities are strictly harder than linear equalities in all ''reasonable'' models of computation.