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”, Algorithmica, volume 68, number 2, February 2014, pages 287–311.

BibTeX

@Article{SteinerGenus_Algorithmica,
  AUTHOR        = {Glencora Borradaile and Erik D. Demaine and Siamak Tazari},
  TITLE         = {Polynomial-Time Approximation Schemes for
                   Subset-Connectivity Problems in Bounded-Genus Graphs},
  JOURNAL       = {Algorithmica},
  journalurl    = {https://www.springer.com/journal/453},
  VOLUME        = 68,
  NUMBER        = 2,
  MONTH         = {February},
  YEAR          = 2014,
  PAGES         = {287--311},

  papers        = {SteinerGenus_STACS2009},
  replaces      = {SteinerGenus_STACS2009},
  doi           = {https://dx.doi.org/10.1007/s00453-012-9662-2},
  dblp          = {https://dblp.org/rec/journals/algorithmica/BorradaileDT14},
  comments      = {This paper is also available from <A HREF="http://dx.doi.org/10.1007/s00453-012-9662-2">SpringerLink</A> and as <A HREF="https://arXiv.org/abs/0902.1043">arXiv:0902.1043</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 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, Klein, and Mathieu (2007) will also be approximable in bounded-genus graphs by our extension.

Comments:

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

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SteinerGenus_STACS2009 (Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs)