A linear-time algorithm to find a pair of arc-disjoint spanning in-arborescence and out-arborescence in a directed acyclic graph

Authors:
Kristóf Bérczi;Satoru Fujishige;Naoyuki Kamiyama
Affiliations:
Department of Operations Research, Eötvös Lorand University, Hungary;Research Institute for Mathematical Sciences, Kyoto University, Japan;Department of Information and System Engineering, Chuo University, Japan
Venue:
Information Processing Letters
Year:
2009

Citing 5
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Abstract

Suppose that we are given a directed graph D=(V,A) with specified vertices r"1,r"2@?V. In this paper, we consider the problem of discerning the existence of a pair of arc-disjoint spanning in-arborescence rooted at r"1 and out-arborescence rooted at r"2, and finding such arborescences if they exist. It is known (Bang-Jensen (1991) [1]) that this problem is NP-complete even if r"1=r"2. As a special case, it is only known (Bang-Jensen (1991) [1]) that this problem in a tournament can be solved in polynomial time. In this paper, we give a linear-time algorithm for this problem in a directed acyclic graph. We also consider an extension of our problem to the case where we have multiple roots for in-arborescences and out-arborescences, respectively.