The mathematics of nonlinear programming
The mathematics of nonlinear programming
A subexponential randomized simplex algorithm (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Linear programming 1: introduction
Linear programming 1: introduction
Unique Sink Orientations of Cubes
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Discrete & Computational Geometry
Random Edge Can Be Exponential on Abstract Cubes
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Unique sink orientations of grids
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Jumping doesn't help in abstract cubes
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Violator spaces: structure and algorithms
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Violator spaces: Structure and algorithms
Discrete Applied Mathematics
A subexponential lower bound for the random facet algorithm for parity games
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Counting unique-sink orientations
Discrete Applied Mathematics
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We show that any linear program (LP) in n nonnegative variables and m equality constraints defines in a natural way a unique sink orientation of the n-dimensional cube. From the sink of the cube, we can either read off an optimal solution to the LP, or we obtain certificates for infeasibility or unboundedness.This reduction complements the implicit local neighborhoods induced by the vertex-edge structure of the feasible region with an explicit neighborhood structure that allows random access to all 2n candidate solutions. Using the currently best sink-finding algorithm for general unique sink orientations, we obtain the fastest deterministic LP algorithm in the RAM model, for the central case n = 2m.