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

TitlePolynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs
Publication TypeJournal Article
Year of Publication2012
AuthorsBorradaile, G., E. D. Demaine, and S. Tazari
JournalAlgorithmica
Date Published06/2012
ISSN1432-0541
Keywordsbounded-genus graphs, polynomial-time approximation scheme, Steiner tree, subset TSP
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(nlogn) time for graphs embedded on both orientable and nonorientable surfaces. This work generalizes the PTAS framework from planar graphs to bounded-genus graphs: any problem that is shown to be approximable by the planar PTAS framework of Borradaile et al. (ACM Trans. Algorithms 5(3), 2009) will also be approximable in bounded-genus graphs by our extension.

URLhttp://link.springer.com/article/10.1007/s00453-012-9662-2/fulltext.html
DOI10.1007/s00453-012-9662-2
Short TitleAlgorithmica