Constructing New Facets of the Consecutive Ones Polytope

Abstract

In this paper we relate the consecutive ones problem to the betweenness problem by pointing out connections between their associated polytopes. We will prove some results about the facet structure of the betweenness polytope and show how facets of this polytope can be used to generate facets of the consecutive ones polytope. Furthermore, the relations with the consecutive ones polytopes will enable us to conclude that the number of facets of the consecutive ones polytope only grows polynomially if the number of columns is fixed. This gives another proof of the fact that the consecutive ones problem is solvable in polynomial time in this case.