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Connected and alternating vectors: Polyhedra and algorithms

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Abstract

Given a graphG = (V, E), leta S, S ∈ L, be the edge set incidence vectors of its nontrivial connected subgraphs.

The extreme points ofℬ = {x ∈ R E: asx ≤ |V(S)| - |S|, S ∈ L} are shown to be integer 0/± 1 and characterized. They are the alternating vectorsb k, k ∈ K, ofG.

WhenG is a tree, the extreme points ofB ≥ 0,b kx ≤ 1,k ∈ K} are shown to be the connected vectors ofG together with the origin. For the four LP's associated withℬ andA, good algorithms are given and total dual integrality ofℬ andA proven.

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Authors and Affiliations

  1. IBM T.J. Watson Research Center, 10598, Yorktown Heights, NY, USA

    Heinz Gröflin

  2. Swiss Federal Institute of Technology, Zurich, Switzerland

    Thomas M. Liebling

Authors
  1. Heinz Gröflin
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  2. Thomas M. Liebling
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On leave from Swiss Federal Institute of Technology, Zurich.

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Gröflin, H., Liebling, T.M. Connected and alternating vectors: Polyhedra and algorithms. Mathematical Programming 20, 233–244 (1981). https://doi.org/10.1007/BF01589348

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  • DOI: https://doi.org/10.1007/BF01589348

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