Affiliation:
1. Texas A&M University, College Station, Texas
2. University College Cork, Cork, Ireland
Abstract
The (parameterized) FEEDBACK VERTEX SET problem on directed graphs (i.e., the DFVS problem) is defined as follows: given a directed graph
G
and a parameter
k
, either construct a feedback vertex set of at most
k
vertices in
G
or report that no such a set exists. It has been a well-known open problem in parameterized computation and complexity whether the DFVS problem is fixed-parameter tractable, that is, whether the problem can be solved in time
f
(
k
)
n
O
(1)
for some function
f
. In this article, we develop new algorithmic techniques that result in an algorithm with running time 4
k
k
!
n
O
(1)
for the DFVS problem. Therefore, we resolve this open problem.
Funder
Division of Computing and Communication Foundations
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
182 articles.
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