Polynomial-time approximation schemes for subset-connectivity problems in bounded genus graphs
Glencora Borradaile, Erik Demaine and Siamak Tazari
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.
Proceedings of the Symposium on Theoretical Aspects of Computer Science (STACS), Freiburg, Germany, 2009.
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