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Trimming of Graphs, with Application to Point Labeling Erlebach, Thomas Hagerup, Torben Jansen, Klaus Minzlaff, Moritz Wolff, Alexander Trimming weighted graphs domino treewidth planar graphs point-feature label placement map labeling polynomial-time approximation schemes For $t,g>0$, a vertex-weighted graph of total weight $W$ is $(t,g)$-trimmable if it contains a vertex-induced subgraph of total weight at least $(1-1/t)W$ and with no simple path of more than $g$ edges. A family of graphs is trimmable if for each constant $t>0$, there is a constant $g=g(t)$ such that every vertex-weighted graph in the family is $(t,g)$-trimmable. We show that every family of graphs of bounded domino treewidth is trimmable. This implies that every family of graphs of bounded degree is trimmable if the graphs in the family have bounded treewidth or are planar. Based on this result, we derive a polynomial-time approximation scheme for the problem of labeling weighted points with nonoverlapping sliding labels of unit height and given lengths so as to maximize the total weight of the labeled points. This settles one of the last major open questions in the theory of map labeling. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Thomas Erlebach and Torben Hagerup and Klaus Jansen and Moritz Minzlaff and Alexander Wolff 2008 Is Part Of LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2008.1350 urn:nbn:de:0030-drops-13509 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1350 eng https://creativecommons.org/licenses/by-nd/3.0/legalcode