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DOI: 10.4230/LIPIcs.STACS.2009.1835
URN: urn:nbn:de:0030-drops-18355
URL: https://drops.dagstuhl.de/opus/volltexte/2009/1835/
Borradaile, Glencora ; Demaine, Erik D. ; Tazari, Siamak
Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs
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Abstract
We present the first polynomial-time approximation schemes (PTASes) for the following subset-connectivity problems in edge-weighted graphs of bounded genus: Steiner tree, low-connectivity survivable-network design, and subset TSP. The schemes run in $O(n \log n)$ time for graphs embedded on both orientable and non-orientable surfaces. This work generalizes the PTAS frameworks of Borradaile, Klein, and Mathieu (2007 and 2006) from planar graphs to bounded-genus graphs: any future problems shown to admit the required structure theorem for planar graphs will similarly extend to bounded-genus graphs.
BibTeX - Entry
@InProceedings{borradaile_et_al:LIPIcs:2009:1835,
author = {Glencora Borradaile and Erik D. Demaine and Siamak Tazari},
title = {{Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {171--182},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Susanne Albers and Jean-Yves Marion},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2009/1835},
URN = {urn:nbn:de:0030-drops-18355},
doi = {10.4230/LIPIcs.STACS.2009.1835},
annote = {Keywords: Polynomial-time approximation scheme, Bounded-genus graph, Embedded graph, Steiner tree, Survivable-network design, Subset TSP}
}
| Keywords: | Polynomial-time approximation scheme, Bounded-genus graph, Embedded graph, Steiner tree, Survivable-network design, Subset TSP | |
| Seminar: | 26th International Symposium on Theoretical Aspects of Computer Science | |
| Issue date: | 2009 | |
| Date of publication: | 19.02.2009 |
