Randomized Simplex Algorithms on Klee-Minty Cubes

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.

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Received: September 2, 1996

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Gärtner, B., Henk, M. & Ziegler, G. Randomized Simplex Algorithms on Klee-Minty Cubes. Combinatorica 18, 349–372 (1998). https://doi.org/10.1007/PL00009827

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  • AMS Subject Classification (1991) Classes:  90C05, 52B12, 68Q25