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Optimization problems with color-induced budget constraints

Author

Listed:
  • Corinna Gottschalk

    (RWTH Aachen University
    Siemens Corporate Technology)

  • Hendrik Lüthen

    (TU Darmstadt)

  • Britta Peis

    (RWTH Aachen University)

  • Andreas Wierz

    (RWTH Aachen University)

Abstract

In 1984, Gabow and Tarjan provided a very elegant and fast algorithm for the following problem: given a matroid defined on a red and blue colored ground set, determine a basis of minimum cost among those with k red elements, or decide that no such basis exists. In this paper, we investigate extensions of this problem from ordinary matroids to the more general notion of poset matroids which take precedence constraints on the ground set into account. We show that the problem on general poset matroids becomes -hard, already if the underlying partially ordered set (poset) consists of binary trees of height two. On the positive side, we present two algorithms: a pseudopolynomial one for integer polymatroids, i.e., the case where the poset consists of disjoint chains, and a polynomial algorithm for the problem to determine a minimum cost ideal of size l with k red elements, i.e., the uniform rank-l poset matroid, on series-parallel posets.

Suggested Citation

  • Corinna Gottschalk & Hendrik Lüthen & Britta Peis & Andreas Wierz, 2018. "Optimization problems with color-induced budget constraints," Journal of Combinatorial Optimization, Springer, vol. 36(3), pages 861-870, October.
    • Handle: RePEc:spr:jcomop:v:36:y:2018:i:3:d:10.1007_s10878-017-0182-5
    DOI: 10.1007/s10878-017-0182-5
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    References listed on IDEAS

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    1. Ulrich Faigle & Walter Kern, 1994. "Computational Complexity of Some Maximum Average Weight Problems with Precedence Constraints," Operations Research, INFORMS, vol. 42(4), pages 688-693, August.
    2. Groenevelt, H., 1991. "Two algorithms for maximizing a separable concave function over a polymatroid feasible region," European Journal of Operational Research, Elsevier, vol. 54(2), pages 227-236, September.
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