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Paper detail

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 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.

preprint2011arXivOpen access
Glencora BorradaileErik D. DemaineSiamak Tazari
Data Structures and AlgorithmsDiscrete Mathematics
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Glencora BorradaileErik D. DemaineSiamak Tazari

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