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  Minimum Fill-in of Sparse Graphs: Kernelization and Approximation

Fomin, F. V., Philip, G., & Villanger, Y. (2011). Minimum Fill-in of Sparse Graphs: Kernelization and Approximation. In S. Chakraborty, & A. Kumar (Eds.), 31st International Conference on Foundations of Software Technology and Theoretical Computer Science (pp. 164-175). Wadern: Schloss Dagstuhl. doi:10.4230/LIPIcs.FSTTCS.2011.164.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0025-7597-F Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0025-7598-D
Genre: Conference Paper

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http://drops.dagstuhl.de/opus/volltexte/2011/3345/ (Publisher version)
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http://drops.dagstuhl.de/doku/urheberrecht1.html (Copyright transfer agreement)
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 Creators:
Fomin, Fedor V.1, Author
Philip, Geevarghese2, Author           
Villanger, Yngve1, Author
Affiliations:
1External Organizations, ou_persistent22              
2Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: The \textscMinimum Fill-in} problem is to decide if a graph can be triangulated by adding at most k edges. The problem has important applications in numerical algebra, in particular in sparse matrix computations. We develop kernelization algorithms for the problem on several classes of sparse graphs. We obtain linear kernels on planar graphs, and kernels of size O(k^{3/2}) in graphs excluding some fixed graph as a minor and in graphs of bounded degeneracy. As a byproduct of our results, we obtain approximation algorithms with approximation ratios O(\log{k}) on planar graphs and O(\sqrt{k}\log{k}) on H-minor-free graphs. These results significantly improve the previously known kernelization and approximation results for \textsc{Minimum Fill-in on sparse graphs.

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Language(s): eng - English
 Dates: 2011-12-01
 Publication Status: Published online
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: DOI: 10.4230/LIPIcs.FSTTCS.2011.164
BibTex Citekey: FominPhilipVillanger2011
URN: urn:nbn:de:0030-drops-33451
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Title: 31st International Conference on Foundations of Software Technology and Theoretical Computer Science
Place of Event: Mumbai, India
Start-/End Date: 2011-12-12 - 2011-12-14

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Title: 31st International Conference on Foundations of Software Technology and Theoretical Computer Science
  Abbreviation : FSTTCS 2011
  Subtitle : FSTTCS 2011, December 12–14, 2011, Mumbai, India
  Other : IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science
Source Genre: Proceedings
 Creator(s):
Chakraborty, Supratik1, Editor
Kumar, Amit1, Editor
Affiliations:
1 External Organizations, ou_persistent22            
Publ. Info: Wadern : Schloss Dagstuhl
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 164 - 175 Identifier: ISBN: 978-3-939897-34-7

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Title: Leibniz International Proceedings in Informatics
  Abbreviation : LIPIcs
Source Genre: Series
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Affiliations:
Publ. Info: -
Pages: - Volume / Issue: 13 Sequence Number: - Start / End Page: - Identifier: -