Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Completely unimodal numberings of a simple polytope
Discrete Applied Mathematics
A subexponential randomized simplex algorithm (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Randomized algorithms
The worst-case running time of the random simplex algorithm is exponential in the height
Information Processing Letters
Linear programming, the simplex algorithm and simple polytopes
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Random Structures & Algorithms
| Hi-index | 0.00 |
We analyze a randomized pivoting process involving one line and n points in the plane. The process models the behavior of the Random-Edge simplex algorithm on simple polytopes with n facets in dimension n-2. We obtain a tight O(\log^2 n) bound for the expected number of pivot steps. This is the first nontrivial bound for Random-Edge which goes beyond bounds for specific polytopes. The process itself can be interpreted as a simple algorithm for certain 2-variable linear programming problems, and we prove a tight &thgr;(n) bound for its expected runtime.The combinatorial structure behind the process is a directed graph over pairs of points, with arc orientations induced by the pivot steps. We characterize the class of graphs arising from one line and n points, up to oriented matroid realizability.