1 research outputs found
New Bounds for the Vertices of the Integer Hull
The vertices of the integer hull are the integral equivalent to the
well-studied basic feasible solutions of linear programs. In this paper we give
new bounds on the number of non-zero components -- their support -- of these
vertices matching either the best known bounds or improving upon them. While
the best known bounds make use of deep techniques, we only use basic results
from probability theory to make use of the concentration of measure effect. To
show the versatility of our techniques, we use our results to give the best
known bounds on the number of such vertices and an algorithm to enumerate them.
We also improve upon the known lower bounds to show that our results are nearly
optimal. One of the main ingredients of our work is a generalization of the
famous Hoeffding bound to vector-valued random variables that might be of
general interest