### A fixed-parameter algorithm for the directed feedback vertex set problemA fixed-parameter algorithm for the directed feedback vertex set problem

Access Restriction
Subscribed

 Author Chen, Jianer ♦ Liu, Yang ♦ Lu, Songjian ♦ Osullivan, Barry ♦ Razgon, Igor Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2008 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Deadlock ♦ Feedback vertex set ♦ Parameterized computation Abstract The (parameterized) FEEDBACK VERTEX SET problem on directed graphs (i.e., the DFVS problem) is defined as follows: given a directed graph $\textit{G}$ and a parameter $\textit{k},$ either construct a feedback vertex set of at most $\textit{k}$ vertices in $\textit{G}$ 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 $\textit{f}.$ In this article, we develop new algorithmic techniques that result in an algorithm with running time $4^{k}$ $\textit{k}!$ $n^{O(1)}$ for the DFVS problem. Therefore, we resolve this open problem. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2008-11-05 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 55 Issue Number 5 Page Count 19 Starting Page 1 Ending Page 19

#### Open content in new tab

Source: ACM Digital Library