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

Kristóf Bérczi, Satoru Fujishige, Naoyuki Kamiyama

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Suppose that we are given a directed graph D = (V, A) with specified vertices r1, r2 ∈ V. In this paper, we consider the problem of discerning the existence of a pair of arc-disjoint spanning in-arborescence rooted at r1 and out-arborescence rooted at r2, and finding such arborescences if they exist. It is known (Bang-Jensen (1991) [1]) that this problem is NP-complete even if r1 = r2. 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.

Original languageEnglish
Pages (from-to)1227-1231
Number of pages5
JournalInformation Processing Letters
Volume109
Issue number23-24
DOIs
Publication statusPublished - Nov 15 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications

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