Trimming of Graphs, with Application to Point Labeling

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dc.creatorErlebach, Thomas
dc.creatorHagerup, Torben
dc.creatorJansen, Klaus
dc.creatorMinzlaff, Moritz
dc.creatorWolff, Alexander
dc.date2008-02-20
dc.date.accessioned2026-07-07T09:22:03Z
dc.date.available2026-07-07T09:22:03Z
dc.descriptionFor $t,g>0$, 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.
dc.identifierhttps://arxiv.org/abs/0802.2854
dc.identifierhttp://arxiv.org/abs/0802.2854
dc.identifierDans Proceedings of the 25th Annual Symposium on the Theoretical Aspects of Computer Science - STACS 2008, Bordeaux : France (2008)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155241
dc.subjectDiscrete Mathematics
dc.subjectData Structures and Algorithms
dc.subjectCombinatorics
dc.titleTrimming of Graphs, with Application to Point Labeling
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