LIPIcs.STACS.2008.1350.pdf
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Trimming of Graphs, with Application to Point Labeling
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25th International Symposium on Theoretical Aspects of Computer Science (STACS 2008)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Theoretical Aspects of Computer Science (STACS) - License:
Creative Commons Attribution-NoDerivs 3.0 Unported license
- Publication Date: 2008-02-06
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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
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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