TY - GEN A1 - Kaibel, Volker A1 - Mechtel, Rafael A1 - Shair, Micha A1 - Ziegler, Günter M. T1 - The Simplex Algorithm in Dimension Three N2 - We investigate the worst-case behavior of the simplex algorithm on linear programs with 3 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 is known to be subexponential without dimension restriction, as well as Zadeh’s deterministic history-dependent rule, for which no non-polynomial instances in general dimensions have been found so far. Y1 - 2004 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/12 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-120 ER -