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.
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References
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M. Oswald and G. Reinelt (2001) Some Relations Between Consecutive Ones and Betweenness Polytopes, to appear in: Proceedings of OR2001, Selected Papers, Duisburg
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© 2003 Springer-Verlag Berlin Heidelberg
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Oswald, M., Reinelt, G. (2003). Constructing New Facets of the Consecutive Ones Polytope. In: Jünger, M., Reinelt, G., Rinaldi, G. (eds) Combinatorial Optimization — Eureka, You Shrink!. Lecture Notes in Computer Science, vol 2570. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36478-1_14
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DOI: https://doi.org/10.1007/3-540-36478-1_14
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