MPI-I-97-2-009
On the Chvátal rank of polytopes in the 0/1 cube
Bockmayr, Alexander and Eisenbrand, Friedrich
September 1997, 12 pages.
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Status: available - back from printing
Given a polytope $P \subseteq \mathbb{R}^n$, the Chv\'atal-Gomory
procedure computes iteratively the integer hull $P_I$ of $P$. The
Chv\'atal rank of $P$ is the minimal number of iterations needed to
obtain $P_I$. It is always finite, but already the Chv\'atal rank of
polytopes in $\mathbb{R}^2$ can be arbitrarily large. In this paper,
we study polytopes in the 0/1~cube, which are of particular interest in
combinatorial optimization. We show that the Chv\'atal rank of a polytope
$P \subseteq [0,1]^n $ in the 0/1~cube is at most $6 n^3 \log n$ and prove
the linear upper and lower bound $n$ for the case $P\cap \mathbb{Z}^n
= \emptyset$.
Categories / Keywords:
combinatorial optimization, integer programming, cutting plane, polytope
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URL to this document: https://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1997-2-009
BibTeX
@TECHREPORT{BockmayrEisenbrand97,
AUTHOR = {Bockmayr, Alexander and Eisenbrand, Friedrich},
TITLE = {On the {Chv{\'a}tal} rank of polytopes in the 0/1 cube},
TYPE = {Research Report},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
NUMBER = {MPI-I-97-2-009},
MONTH = {September},
YEAR = {1997},
ISSN = {0946-011X},
}