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. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Berger, A., Czumaj, A., Grigni, M., & Zhao, H. (2005). Approximation schemes for minimum 2-connected spanning subgraphs in weighted planar graphs. In Lecture Notes in Computer Science (Vol. 3669, pp. 472–483). Springer Verlag. https://doi.org/10.1007/11561071_43
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