ISCO 2016: Combinatorial Optimization pp 189-200

# Optimization Problems with Color-Induced Budget Constraints

• Corinna Gottschalk
• Hendrik Lüthen
• Britta Peis
• Andreas Wierz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9849)

## Abstract

Gabow and Tarjan [9] 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 possible extensions of this result from ordinary matroids to the more general notion of poset matroids. Poset matroids (also called distributive supermatroids) are defined on the collection of all ideals of an underlying partial order on the ground set. We show that the problem on general poset matroids becomes NP-hard, already if the underlying poset consists of binary trees of height two. On the positive side, we present two polynomial algorithms: one for integer polymatroids, i.e., the case where the poset consists of disjoint chains, and one 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.

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© Springer International Publishing Switzerland 2016

## Authors and Affiliations

• Corinna Gottschalk
• 1
Email author
• Hendrik Lüthen
• 2
• Britta Peis
• 1
• Andreas Wierz
• 1
1. 1.RWTH Aachen UniversityAachenGermany