A new polynomial-time algorithm for linear programming
Combinatorica
Mathematical Programming: Series A and B
A strongly polynomial algorithm to solve combinatorial linear programs
Operations Research
Theory of linear and integer programming
Theory of linear and integer programming
A probabilistic analysis of the simplex method
A probabilistic analysis of the simplex method
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
An introduction to structured modeling
Management Science
Expressing combinatorial optimization problems by linear programs
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
A subexponential bound for linear programming
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
.879-approximation algorithms for MAX CUT and MAX 2SAT
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Randomized algorithms
A parallel algorithm for linear programming in fixed dimension
Proceedings of the eleventh annual symposium on Computational geometry
Proceedings of the eighth annual ACM symposium on Parallel algorithms and architectures
Primal-dual interior-point methods
Primal-dual interior-point methods
Algorithms for the optimal loading of recursive neural nets
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Journal of the ACM (JACM)
Linear Programming in Linear Time When the Dimension Is Fixed
Journal of the ACM (JACM)
Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Introduction to Linear Optimization
Introduction to Linear Optimization
Neural Networks and Complexity Theory
MFCS '92 Proceedings of the 17th International Symposium on Mathematical Foundations of Computer Science
A Combinatorial Bound for Linear Programming and Related Problems
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
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Linear programming has been a fundamental topic in the development of computational sciences. The subject has its origins in the early work of L. B. J. Fourier on solving systems of linear inequalities, dating back to the 1820s. More recently, a healthy competition between the simplex and interior point methods has led to rapid improvements in the technologies of linear programming. This combined with remarkable advances in computing hardware and software have brought linear programming tools to the desktop, in a variety of application software for decision support. Linear programming has provided a fertile ground for the development of various algorithmic paradigms. Diverse topics such as symbolic computation, numerical analysis, computational complexity, computational geometry, combinatorial optimization, and randomized algorithms all have some linear programming connection. This chapter reviews this universal role played by linear programming in the science of algorithms.