Work

Blocking optimal $k$-arborescences

Year: 2015

Type: conference-paper

Abstract: Given a digraph $D=(V,A)$ and a positive integer $k$, an arc set $F\subseteq A$ is called a \textbf{$k$-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.

Source: Repository of the Academy's Library (Library of the Hungarian Academy of Sciences)

DOI: 10.48550/arxiv.1507.04207

Authors: Bernáth, Attila, Király, Tamás

Institution: Eötvös Loránd University

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Hungarian Scientific Research Fund

Award: G6063911051