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 \(\mathcal{O}(n \log n)\) 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.
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