Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs
Author(s)Borradaile, Glencora; Demaine, Erik D.; Tazari, Siamak
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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(nlogn) 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.
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Springer-Verlag Berlin Heidelberg
Borradaile, Glencora, Erik D. Demaine, and Siamak Tazari. “Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs.” Algorithmica 68, no. 2 (February 2014): 287–311. doi:10.1007/s00453-012-9662-2.
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