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Packing and covering a tree by subtrees

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Abstract

For two polyhedra associated with packing subtrees of a tree, the structure of the vertices is described, and efficient algorithms are given for optimisation over the polyhedra. For the related problem of covering a tree by subtrees, a reduction to a packing problem, and an efficient algorithm are presented when the family of trees is “fork-free”.

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References

  1. I. Bárány, T. J. Van Roy, andL. A. Wolsey, Uncapacitated Lot-Sizing: The Convex Hull-of Solutions,Mathematical Programming Study,22 (1984), 32–43.

    MATH  Google Scholar 

  2. A. Frank, Some Polynomial Algorithms for Certain Graphs and Hypergraphs,Proceedings of the 5th British Combinatorial Conference, Congressus Numerantium XV,Utilitas Math., Winnipeg (1976).

  3. F. Gavril, The intersection Graphs of Subtrees in Trees are Exactly the Chordal Graphs,Journal of Combinatorial Theory, B 16, (1974), 47–56.

    Article  MATH  MathSciNet  Google Scholar 

  4. M. C. Golumbic,Algorithmic Graph Theory and Perfect Graphs, Academic Press, (1980).

  5. H. Gröflin andT. M. Liebling, Connected and Alternating Vectors: Polyhedra and Algorithms,Mathematical Programming,20 (1981), 233–244.

    Article  MATH  MathSciNet  Google Scholar 

  6. A. J. Hoffman, A. W. J. Kolen andM. Sakarovitch, Totally Balanced and Greedy Matrices,Prepring BW 165/82,Stiching Mathematisch Centrum, Amsterdam, (1982).

  7. A. W. J. Kolen, Solving Covering Problems and the Uncapacitated Plant Location Problem on Trees,Preprint BW 163/82,Stichting Mathematisch Centrum, Amsterdam (1982).

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Author information

Authors and Affiliations

  1. Mathematical Institute of the Hungarian Academy of Sciences, Reáltanoda u. 13–15, 1053, Hungary

    I. Bárány

  2. Center Op. Res, Econometrics, Université Catholique de Louvain, 1348, Louvain-la-Neuve, Belgium

    L. A. Wolsey

  3. Dept. of Combinatorics and Optimization, University of Waterloo, Ontario, Canada

    J. Edmonds

Authors
  1. I. Bárány
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  2. L. A. Wolsey
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  3. J. Edmonds
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Bárány, I., Wolsey, L.A. & Edmonds, J. Packing and covering a tree by subtrees. Combinatorica 6, 221–233 (1986). https://doi.org/10.1007/BF02579383

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  • DOI: https://doi.org/10.1007/BF02579383

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