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Blocking Optimal k-Arborescences

机译:阻止最佳k-arborbecences

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摘要

Given a digraph D = (V, A) and a positive integer k, an arc set F C 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. Bernath, 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.
机译:给定D =(V,A)和正整数k,如果是K跨越树丛的不相交联盟,则弧形集F C a被称为k轴突。已知找到最小成本K-恒星的问题是使用MATROID交叉点的多项式溶解。在本文中,我们研究了以下问题:找到包含至少一个来自每个最小成本k轴轴的电弧的最小基数子集。对于k = 1. [A.]解决了问题Bernath,G.Pap,阻止最佳arborescences,IPCO 2013]。在本文中,我们为一般k提供了一种具有多项式运行时间的一般k的算法。

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