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arXiv · 0902.1043

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

Glencora Borradaile·Erik D. Demaine·Siamak Tazari
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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 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, Siamak Tazari. 2009-02-06. Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs. https://arxiv.org/abs/0902.1043

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