Affiliation:
1. KAIST, Daejeon, Republic of Korea
Abstract
Rank-width was defined by Oum and Seymour [2006] to investigate clique-width. They constructed an algorithm that either outputs a rank-decomposition of width at most
f
(
k
) for some function
f
or confirms that rank-width is larger than
k
in time
O
(|
V
|
9
log |
V
|) for an input graph
G
= (
V
,
E
) and a fixed
k
. We develop three separate algorithms of this kind with faster running time. We construct an
O
(|
V
|
4
)-time algorithm with
f
(
k
) = 3
k
+ 1 by constructing a subroutine for the previous algorithm; we avoid generic algorithms minimizing submodular functions used by Oum and Seymour. Another one is an
O
(|
V
|
3
)-time algorithm with
f
(
k
) = 24
k
, achieved by giving a reduction from graphs to binary matroids; then we use an approximation algorithm for matroid branch-width by Hliněný [2005]. Finally we construct an
O
(|
V
|
3
)-time algorithm with
f
(
k
) = 3
k
− 1 by combining the ideas of the two previously cited papers.
Funder
Ministry of Science and Technology
National Science Foundation
Publisher
Association for Computing Machinery (ACM)
Subject
Mathematics (miscellaneous)
Cited by
77 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献