Publication Date:
2014-11-21
Description:
We prove that the Random-Edge simplex algorithm requires an expected number of at most $13n/sqrt(d)$ pivot steps on any simple d-polytope with n vertices. This is the first nontrivial upper bound for general polytopes. We also describe a refined analysis that potentially yields much better bounds for specific classes of polytopes. As one application, we show that for combinatorial d-cubes, the trivial upper bound of $2^d$ on the performance of Random-Edge can asymptotically be improved by any desired polynomial factor in d.
Keywords:
ddc:000
Language:
English
Type:
reportzib
,
doc-type:preprint
Format:
application/pdf
Format:
application/postscript
Permalink