The Simplex Algorithm in Dimension Three

Details The Simplex Algorithm in Dimension Three The Simplex Algorithm in Dimension Three

2003-09-22

arxiv.org/abs/math/0309351v2

Mathematics

Combinatorics

24 pages, to appear in: SIAM J. Comp.; the paper comprises the contents of our paper 'The Random Edge Rule on Three-Dimensiona

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The Simplex Algorithm in Dimension Three does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Simplex Algorithm in Dimension Three, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Simplex Algorithm in Dimension Three will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-161304