Covering directed graphs by in-trees

Naoyuki Kamiyama, Naoki Katoh

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

Given a directed graph D = (V,A) with a set of d specified vertices S = {s1,...,s d }⊆ V and a function f: S → ℤ+ where ℤ+ denotes the set of non-negative integers, we consider the problem which asks whether there exist ∑i=1d f (si) in-trees denoted by T i, 1, Ti, 2, ..., Ti f(si) for every i = 1,...,d such that Ti, 1,...,Ti, f(si) are rooted at s i, each Ti,j spans vertices from which s i is reachable and the union of all arc sets of Ti,j for i = 1,...,d and j = 1,...,f(si ) covers A. In this paper, we prove that such set of in-trees covering A can be found by using an algorithm for the weighted matroid intersection problem in time bounded by a polynomial in ∑i=1d f (si) and the size of D. Furthermore, for the case where D is acyclic, we present another characterization of the existence of in-trees covering A, and then we prove that in-trees covering A can be computed more efficiently than the general case by finding maximum matchings in a series of bipartite graphs.

Original languageEnglish
Title of host publicationComputing and Combinatorics - 14th Annual International Conference, COCOON 2008, Proceedings
Pages444-457
Number of pages14
DOIs
Publication statusPublished - Aug 4 2008
Event14th Annual International Conference on Computing and Combinatorics, COCOON 2008 - Dalian, China
Duration: Jun 27 2008Jun 29 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5092 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other14th Annual International Conference on Computing and Combinatorics, COCOON 2008
CountryChina
CityDalian
Period6/27/086/29/08

Fingerprint

Covering Graph
Directed graphs
Directed Graph
Polynomials
Covering
Matroid Intersection
Maximum Matching
Bipartite Graph
Arc of a curve
Union
Non-negative
Cover
Denote
Polynomial
Integer
Series

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Kamiyama, N., & Katoh, N. (2008). Covering directed graphs by in-trees. In Computing and Combinatorics - 14th Annual International Conference, COCOON 2008, Proceedings (pp. 444-457). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5092 LNCS). https://doi.org/10.1007/978-3-540-69733-6_44

Covering directed graphs by in-trees. / Kamiyama, Naoyuki; Katoh, Naoki.

Computing and Combinatorics - 14th Annual International Conference, COCOON 2008, Proceedings. 2008. p. 444-457 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5092 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kamiyama, N & Katoh, N 2008, Covering directed graphs by in-trees. in Computing and Combinatorics - 14th Annual International Conference, COCOON 2008, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5092 LNCS, pp. 444-457, 14th Annual International Conference on Computing and Combinatorics, COCOON 2008, Dalian, China, 6/27/08. https://doi.org/10.1007/978-3-540-69733-6_44
Kamiyama N, Katoh N. Covering directed graphs by in-trees. In Computing and Combinatorics - 14th Annual International Conference, COCOON 2008, Proceedings. 2008. p. 444-457. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-540-69733-6_44
Kamiyama, Naoyuki ; Katoh, Naoki. / Covering directed graphs by in-trees. Computing and Combinatorics - 14th Annual International Conference, COCOON 2008, Proceedings. 2008. pp. 444-457 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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