Approximation Schemes for Minimum 2-Connected Spanning Subgraphs in Weighted Planar Graphs

  • André Berger
  • Artur Czumaj
  • Michelangelo Grigni
  • Hairong Zhao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3669)


We present new approximation schemes for various classical problems of finding the minimum-weight spanning subgraph in edge-weighted undirected planar graphs that are resistant to edge or vertex removal. We first give a PTAS for the problem of finding minimum-weight 2-edge-connected spanning subgraphs where duplicate edges are allowed. Then we present a new greedy spanner construction for edge-weighted planar graphs, which augments any connected subgraph A of a weighted planar graph G to a (1+ε)-spanner of G with total weight bounded by weight(A)/ε. From this we derive quasi-polynomial time approximation schemes for the problems of finding the minimum-weight 2-edge-connected or biconnected spanning subgraph in planar graphs. We also design approximation schemes for the minimum-weight 1-2-connectivity problem, which is the variant of the survivable network design problem where vertices have 1 or 2 connectivity constraints. Prior to our work, for all these problems no polynomial or quasi-polynomial time algorithms were known to achieve an approximation ratio better than 2.


Planar Graph Approximation Scheme Jordan Curve Span Subgraph Connectivity Problem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • André Berger
    • 1
  • Artur Czumaj
    • 2
  • Michelangelo Grigni
    • 1
  • Hairong Zhao
    • 2
  1. 1.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA
  2. 2.Department of Computer ScienceNew Jersey Institute of TechnologyNewarkUSA

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