Directed Acyclic Subgraph Problem Parameterized above the Poljak-Turzik Bound

Crowston, Robert; Gutin, Gregory; Jones, Mark

doi:10.4230/LIPIcs.FSTTCS.2012.400

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Directed Acyclic Subgraph Problem Parameterized above the Poljak-Turzik Bound

Authors Robert Crowston, Gregory Gutin, Mark Jones

Part of: Volume: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS)
License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
Publication Date: 2012-12-14

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Document Identifiers

DOI: 10.4230/LIPIcs.FSTTCS.2012.400
URN: urn:nbn:de:0030-drops-38765

Subject Classification

Keywords

Acyclic Subgraph
Fixed-parameter tractable
Polynomial Kernel

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Abstract

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).

Cite As Get BibTex

Robert Crowston, Gregory Gutin, and Mark Jones. Directed Acyclic Subgraph Problem Parameterized above the Poljak-Turzik Bound. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 400-411, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012) https://doi.org/10.4230/LIPIcs.FSTTCS.2012.400

Author Details

Robert Crowston

Gregory Gutin

Mark Jones

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