## Randomized Simplex Algorithms on Klee-Minty Cubes (1994)

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### Other Repositories/Bibliography

Venue: | COMBINATORICA |

Citations: | 19 - 6 self |

### BibTeX

@ARTICLE{Gärtner94randomizedsimplex,

author = {Bernd Gärtner and Martin Henk and Günter M. Ziegler},

title = {Randomized Simplex Algorithms on Klee-Minty Cubes},

journal = {COMBINATORICA},

year = {1994},

volume = {18},

pages = {502--510}

}

### Years of Citing Articles

### OpenURL

### Abstract

We investigate the behavior of randomized simplex algorithms on special linear programs. For this, we use combinatorial models for the Klee-Minty cubes [22] and similar linear programs with exponential decreasing paths. The analysis of two most natural randomized pivot rules on the Klee-Minty cubes leads to (nearly) quadratic lower bounds for the complexity of linear programming with random pivots. Thus we disprove two bounds (for the expected running time of the random-edge simplex algorithm on Klee-Minty cubes) conjectured in the literature. At the same time, we establish quadratic upper bounds for the expected length of a path for a simplex algorithm with random pivots on the classes of linear programs under investigation. In contrast to this, we find that the average length of an increasing path in a Klee-Minty cube is exponential when all paths are taken with equal probability.