math_groups_discgeom

The simplex algorithm in dimension three

Volker Kaibel and Rafael Mechtel and Micha Sharir and Günter M. Ziegler— 2005

We investigate the worst-case behavior of the simplex algorithm on linear programs with three variables, that is, on 3-dimensional simple polytopes. Among the pivot rules that we consider, the ``random edge'' rule yields the best asymptotic behavior as well as the most complicated analysis. All other rules turn out to be much easier to study, but also produce worse results: Most of them show essentially worst-possible behavior; this includes both Kalai's ``random-facet'' rule, which without dimension restriction is known to be subexponential, as well as Zadeh's deterministic history dependent rule, for which no non-polynomial instances in general dimensions have been found so far.

TitelThe simplex algorithm in dimension three
VerfasserVolker Kaibel and Rafael Mechtel and Micha Sharir and Günter M. Ziegler
Datum2005
Quelle/n
Erschienen inSIAM J. Computing, volume 34, pages 475--497
ArtText