Fomin, Fedor V. ;
Philip, Geevarghese ;
Villanger, Yngve
Minimum Fillin of Sparse Graphs: Kernelization and Approximation
Abstract
The Minimum Fillin 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 Hminorfree graphs. These results significantly improve the previously known kernelization and approximation results for Minimum Fillin on sparse graphs.
BibTeX  Entry
@InProceedings{fomin_et_al:LIPIcs:2011:3345,
author = {Fedor V. Fomin and Geevarghese Philip and Yngve Villanger},
title = {{Minimum Fillin of Sparse Graphs: Kernelization and Approximation}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)},
pages = {164175},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783939897347},
ISSN = {18688969},
year = {2011},
volume = {13},
editor = {Supratik Chakraborty and Amit Kumar},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2011/3345},
URN = {urn:nbn:de:0030drops33451},
doi = {http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2011.164},
annote = {Keywords: Minimum FillIn, Approximation, Kernelization, Sparse graphs }
}
2011
Keywords: 

Minimum FillIn, Approximation, Kernelization, Sparse graphs 
Seminar: 

IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)

Related Scholarly Article: 


Issue date: 

2011 
Date of publication: 

2011 