eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2012-12-14
400
411
10.4230/LIPIcs.FSTTCS.2012.400
article
Directed Acyclic Subgraph Problem Parameterized above the Poljak-Turzik Bound
Crowston, Robert
Gutin, Gregory
Jones, Mark
An oriented graph is a directed graph without directed 2-cycles. Poljak and Turzik (1986) proved that every connected oriented graph G on n vertices and m arcs contains an acyclic subgraph with at least m/2+(n-1)/4 arcs. Raman and Saurabh (2006) gave another proof of this result and left it as an open question to establish the parameterized complexity of the following problem: does G have an acyclic subgraph with least m/2 + (n-1)/4 + k arcs, where k is the parameter? We answer this question by showing that the problem can be solved by an algorithm of runtime (12k)!n^{O(1)}. Thus, the problem is fixed-parameter tractable. We also prove that there is a polynomial time algorithm that either establishes that the input instance of the problem is a Yes-instance or reduces the input instance to an equivalent one of size O(k^2).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol018-fsttcs2012/LIPIcs.FSTTCS.2012.400/LIPIcs.FSTTCS.2012.400.pdf
Acyclic Subgraph
Fixed-parameter tractable
Polynomial Kernel