Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs

Borradaile, Glencora; Demaine, Erik D.; Tazari, Siamak

doi:10.4230/LIPIcs.STACS.2009.1835

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Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs

Authors Glencora Borradaile, Erik D. Demaine, Siamak Tazari

Part of: Volume: 26th International Symposium on Theoretical Aspects of Computer Science (STACS 2009)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Symposium on Theoretical Aspects of Computer Science (STACS)
License: Creative Commons Attribution-NoDerivs 3.0 Unported license
Publication Date: 2009-02-19

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DOI: 10.4230/LIPIcs.STACS.2009.1835
URN: urn:nbn:de:0030-drops-18355

Subject Classification

Keywords

Polynomial-time approximation scheme
Bounded-genus graph
Embedded graph
Steiner tree
Survivable-network design
Subset TSP

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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.

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Glencora Borradaile, Erik D. Demaine, and Siamak Tazari. Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 171-182, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009) https://doi.org/10.4230/LIPIcs.STACS.2009.1835

Author Details

Glencora Borradaile

Erik D. Demaine

Siamak Tazari

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