Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs
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.
Polynomial-time approximation scheme
Bounded-genus graph
Embedded graph
Steiner tree
Survivable-network design
Subset TSP
171-182
Regular Paper
Glencora
Borradaile
Glencora Borradaile
Erik D.
Demaine
Erik D. Demaine
Siamak
Tazari
Siamak Tazari
10.4230/LIPIcs.STACS.2009.1835
Creative Commons Attribution-NoDerivs 3.0 Unported license
https://creativecommons.org/licenses/by-nd/3.0/legalcode