Paper by Erik D. Demaine

Reference:

Glencora Borradaile, Erik D. Demaine, and Siamak Tazari, “Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs”, in Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS 2009), Freiburg, Germany, February 26–28, 2009, pages 171–182.

BibTeX

@InProceedings{SteinerGenus_STACS2009,
  AUTHOR        = {Glencora Borradaile and Erik D. Demaine and Siamak Tazari},
  TITLE         = {Polynomial-Time Approximation Schemes for
                   Subset-Connectivity Problems in Bounded-Genus Graphs},
  BOOKTITLE     = {Proceedings of the 26th International Symposium on
                   Theoretical Aspects of Computer Science (STACS 2009)},
  bookurl       = {http://stacs2009.informatik.uni-freiburg.de/},
  ADDRESS       = {Freiburg, Germany},
  MONTH         = {February 26--28},
  YEAR          = 2009,
  PAGES         = {171--182},

  papers        = {SteinerGenus_Algorithmica},
  copyright     = {Copyright held by the authors.  Licensed under the
                   <A HREF="http://creativecommons.org/licenses/by-nd/3.0/">Creative Commons Attribution-No Derivative Works 3.0</A> license.},
  doi           = {https://dx.doi.org/10.4230/LIPIcs.STACS.2009.1835},
  dblp          = {https://dblp.org/rec/conf/stacs/BorradaileDT09},
  comments      = {This paper is also available as <A HREF="https://arXiv.org/abs/0902.1043">arXiv:0902.1043</A>, and from <A HREF="https://doi.org/10.4230/LIPIcs.STACS.2009.1835">LIPIcs</A>.},
}

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 [BMK07, Kle06] 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.

Comments:

This paper is also available as arXiv:0902.1043, and from LIPIcs.

Copyright:

Copyright held by the authors. Licensed under the Creative Commons Attribution-No Derivative Works 3.0 license.

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