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# Trimming of Graphs, with Application to Point Labeling

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LIPIcs.STACS.2008.1350.pdf
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## Cite As

Thomas Erlebach, Torben Hagerup, Klaus Jansen, Moritz Minzlaff, and Alexander Wolff. Trimming of Graphs, with Application to Point Labeling. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 265-276, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
https://doi.org/10.4230/LIPIcs.STACS.2008.1350

## Abstract

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.
##### Keywords
• Trimming weighted graphs
• domino treewidth
• planar graphs
• point-feature label placement
• map labeling
• polynomial-time approximation schemes

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