A new polynomial-time algorithm for linear programming
Combinatorica
Linear programming in O(n × 3d2) time
Information Processing Letters
On a multidimensional search technique and its application to the Euclidean one centre problem
SIAM Journal on Computing
Theory of linear and integer programming
Theory of linear and integer programming
Small-dimensional linear programming and convex hulls made easy
Discrete & Computational Geometry
A subexponential randomized simplex algorithm (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
A subexponential bound for linear programming
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Randomized algorithms
Linear Programming in Linear Time When the Dimension Is Fixed
Journal of the ACM (JACM)
A Combinatorial Bound for Linear Programming and Related Problems
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
The random facet simplex algorithm on combinatorial cubes
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
A Discrete Subexponential Algorithm for Parity Games
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Subexponential lower bounds for randomized pivoting rules for the simplex algorithm
Proceedings of the forty-third annual ACM symposium on Theory of computing
A subexponential lower bound for the random facet algorithm for parity games
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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Three papers were published in 1992, each providing a combinatorial, randomized algorithm solving linear programming in subexponential expected time. Bounds on independent algorithms were proven, one by Kalai, and the other by Matousek, Sharir, and Welzl. Results by Gärtner combined techniques from these papers to solve a much more general optimization problem in similar time bounds.Although the algorithms by Kalai and Sharir-Welzl seem remarkably different in style and evolution, this paper demonstrates that one of the variants of Kalai's algorithm is identical (although dual) to the algorithm of Sharir-Welzl. Also the implication of Gärtner's framework on future improvements is examined more carefully.