English

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

Discrete Mathematics 2011-03-02 v2 Data Structures and Algorithms

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.

Keywords

Cite

@article{arxiv.0902.1043,
  title  = {Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs},
  author = {Glencora Borradaile and Erik D. Demaine and Siamak Tazari},
  journal= {arXiv preprint arXiv:0902.1043},
  year   = {2011}
}

Comments

Updated version from the conference (STACS) version

R2 v1 2026-06-21T12:08:32.084Z