License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.07281.6
URN: urn:nbn:de:0030-drops-12353
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2007/1235/
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Raible, Daniel ; Fernau, Henning

Exact Elimination of Cycles in Graphs

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07281.RaibleDaniel.Paper.1235.pdf (0.3 MB)

Abstract

One of the standard basic steps in drawing hierarchical graphs
is to invert some arcs of the given graph to make the graph acyclic.
We discuss exact and parameterized algorithms for this problem. In particular we examine a graph class called $(1,n)$-graphs, which contains cubic graphs. For both exact and parameterized algorithms we use a non-standard measure approach for the analysis. The analysis of the parameterized algorithm is of special interest, as it is not an amortized analysis modelled by 'finite states' but rather a 'top-down' amortized analysis. For $(1,n)$-graphs we achieve a running time of $Oh^*(1.1871^m)$ and $Oh^*(1.212^k)$, for cubic graphs $Oh^*(1.1798^m)$ and $Oh^*(1.201^k)$, respectively. As a by-product the trivial bound of $2^n$ for {sc Feedback Vertex Set} on planar directed graphs is broken.

BibTeX - Entry

@InProceedings{raible_et_al:DagSemProc.07281.6,
  author =	{Raible, Daniel and Fernau, Henning},
  title =	{{Exact Elimination of Cycles in Graphs}},
  booktitle =	{Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs},
  pages =	{1--25},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7281},
  editor =	{Erik Demaine and Gregory Z. Gutin and Daniel Marx and Ulrike Stege},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2007/1235},
  URN =		{urn:nbn:de:0030-drops-12353},
  doi =		{10.4230/DagSemProc.07281.6},
  annote =	{Keywords: Maximum Acyclic Subgraph, Feedback Arc Set, Amortized Analysis, Exact exponential algorthms}
}

Keywords: Maximum Acyclic Subgraph, Feedback Arc Set, Amortized Analysis, Exact exponential algorthms
Collection: 07281 - Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs
Issue Date: 2007
Date of publication: 28.11.2007

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