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A polyhedron with alls—t cuts as vertices, and adjacency of cuts

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Abstract

Consider the polyhedron represented by the dual of the LP formulation of the maximums–t flow problem. It is well known that the vertices of this polyhedron are integral, and can be viewed ass–t cuts in the given graph. In this paper we show that not alls–t cuts appear as vertices, and we give a characterization. We also characterize pairs of cuts that form edges of this polyhedron. Finally, we show a set of inequalities such that the corresponding polyhedron has as its vertices alls–t cuts.

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Authors and Affiliations

  1. Max Planck Institut für Informatik, Im Stadtwald, D-66123, Saarbrücken, Germany

    Naveen Garg

  2. College of Computing, Georgia Institute of Technology, Atlanta, GA, USA

    Vijay V. Vazirani

Authors
  1. Naveen Garg
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  2. Vijay V. Vazirani
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Additional information

Work done at the Department of Computer Science and Engineering, Indian Institute of Technology, Delhi, India.

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Garg, N., Vazirani, V.V. A polyhedron with alls—t cuts as vertices, and adjacency of cuts. Mathematical Programming 70, 17–25 (1995). https://doi.org/10.1007/BF01585926

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  • DOI: https://doi.org/10.1007/BF01585926

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