Optimization problems with color-induced budget constraints

Corinna Gottschalk, Hendrik Lüthen (), Britta Peis and Andreas Wierz
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Corinna Gottschalk: RWTH Aachen University
Hendrik Lüthen: TU Darmstadt
Britta Peis: RWTH Aachen University
Andreas Wierz: RWTH Aachen University

Journal of Combinatorial Optimization, 2018, vol. 36, issue 3, No 10, 870 pages

Abstract: 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.

Keywords: Budget constrained optimization; Poset matroids; Integer polymatroids; Posets (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10878-017-0182-5

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