A new polynomial-time algorithm for linear programming
Combinatorica
Theory of linear and integer programming
Theory of linear and integer programming
Criss-cross methods: a fresh view on pivot algorithms
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Journal of the ACM (JACM)
A simple polynomial-time rescaling algorithm for solving linear programs
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Solving convex programs by random walks
Journal of the ACM (JACM)
Improved Smoothed Analysis of the Shadow Vertex Simplex Method
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Proceedings of the 5th international conference on Generative programming and component engineering
Iteratively constructing preconditioners via the conjugate gradient method
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Component Updates as a Boolean Optimization Problem
Electronic Notes in Theoretical Computer Science (ENTCS)
CP-summary: a concise representation for browsing frequent itemsets
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Mining discrete patterns via binary matrix factorization
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Smoothed analysis: an attempt to explain the behavior of algorithms in practice
Communications of the ACM - A View of Parallel Computing
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
Subexponential lower bounds for randomized pivoting rules for the simplex algorithm
Proceedings of the forty-third annual ACM symposium on Theory of computing
George Dantzig's impact on the theory of computation
Discrete Optimization
Hi-index | 0.00 |
We present the first randomized polynomial-time simplex algorithm for linear programming. Like the other known polynomial-time algorithms for linear programming, its running time depends polynomially on the number of bits used to represent its input.We begin by reducing the input linear program to a special form in which we merely need to certify boundedness. As boundedness does not depend upon the right-hand-side vector, we run the shadow-vertex simplex method with a random right-hand-side vector. Thus, we do not need to bound the diameter of the original polytope.Our analysis rests on a geometric statement of independent interest: given a polytope A x ≤ b in isotropic position, if one makes a polynomially small perturbation to b then the number of edges of the projection of the perturbed polytope onto a random 2-dimensional subspace is expected to be polynomial.