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DOI: 10.4230/LIPIcs.FSTTCS.2009.2326
A Fine-grained Analysis of a Simple Independent Set Algorithm

Authors: Joachim Kneis, Alexander Langer, and Peter Rossmanith

Published in: LIPIcs, Volume 4, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)

Abstract
We present a simple exact algorithm for the \is\ problem with a runtime bounded by $O(\rt^n \poly(n))$. This bound is obtained by, firstly, applying a new branching rule and, secondly, by a distinct, computer-aided case analysis. The new branching rule uses the concept of satellites and has previously only been used in an algorithm for sparse graphs. The computer-aided case analysis allows us to capture the behavior of our algorithm in more detail than in a traditional analysis. The main purpose of this paper is to demonstrate how a very simple algorithm can outperform more complicated ones if the right analysis of its running time is performed.
Cite as

Joachim Kneis, Alexander Langer, and Peter Rossmanith. A Fine-grained Analysis of a Simple Independent Set Algorithm. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 287-298, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{kneis_et_al:LIPIcs.FSTTCS.2009.2326,
  author =	{Kneis, Joachim and Langer, Alexander and Rossmanith, Peter},
  title =	{{A Fine-grained Analysis of a Simple Independent Set Algorithm}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{287--298},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-13-2},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{4},
  editor =	{Kannan, Ravi and Narayan Kumar, K.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2326},
  URN =		{urn:nbn:de:0030-drops-23269},
  doi =		{10.4230/LIPIcs.FSTTCS.2009.2326},
  annote =	{Keywords: Exact Algorithms, Independent Set, Computer-aided Proof}
}
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