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 [BMK07, Kle06] 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.

• Type: Conference
• Year: 2009
• Where: STACS
• Authors: Glencora Borradaile, Erik D. Demaine, Siamak Tazari
• Keywords: Bounded-genus Graphs, Planar Graphs, STACS 2009, Theoretical Computer Science, first Polynomial-time Approximation