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

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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Submitted on : Thursday, February 5, 2009 - 2:52:36 PM
Last modification on : Wednesday, September 7, 2022 - 3:36:04 PM
Long-term archiving on: : Tuesday, June 8, 2010 - 9:55:45 PM


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  • HAL Id : inria-00359068, version 1
  • ARXIV : 0902.1043



Glencora Borradaile, Erik D. Demaine, Siamak Tazari. Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs. 26th International Symposium on Theoretical Aspects of Computer Science STACS 2009, Feb 2009, Freiburg, Germany. pp.171-182. ⟨inria-00359068⟩



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