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Minimum Fill-in of Sparse Graphs: Kernelization and Approximation Fomin, Fedor V. Philip, Geevarghese Villanger, Yngve Minimum Fill-In Approximation Kernelization Sparse graphs The Minimum 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 Minimum Fill-in on sparse graphs. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Fedor V. Fomin and Geevarghese Philip and Yngve Villanger 2011 Is Part Of LIPIcs, Volume 13, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2011.164 urn:nbn:de:0030-drops-33451 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2011.164 eng https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode