Blocking optimal k-arborescences

Bernáth, Attila and Király, Tamás (2015) Blocking optimal k-arborescences. In: ACM-SIAM Symposium on Discrete Algorithms (SODA16), 10-12 January 2016, Arlington, Virginia, USA. (Submitted)

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Abstract

Given a digraph $D=(V,A)$ and a positive integer $k$, an arc set $F\subseteq A$ is called a $k$-arborescence if it is the disjoint union of $k$ spanning arborescences. The problem of finding a minimum cost $k$-arborescence is known to be polynomial-time solvable using matroid intersection. In this paper we study the following problem: find a minimum cardinality subset of arcs that contains at least one arc from every minimum cost $k$-arborescence. For $k=1$, the problem was solved in [A. Bernáth, G. Pap , Blocking optimal arborescences, IPCO 2013]. In this paper we give an algorithm for general $k$ that has polynomial running time if $k$ is fixed.

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