Approximation schemes for minimum 2-edge-connected and biconnected subgraphs in planar graphs

@inproceedings{Czumaj2004ApproximationSF,
  title={Approximation schemes for minimum 2-edge-connected and biconnected subgraphs in planar graphs},
  author={Artur Czumaj and Michelangelo Grigni and Papa Sissokho and Hairong Zhao},
  booktitle={SODA},
  year={2004}
}
Given an undirected graph, finding either a minimum 2-edge-connected spanning subgraph or a minimum 2-vertex-connected (biconnected) spanning subgraph is MaxSNP-hard. We show that for planar graphs, both problems have a polynomial time approximation scheme (PTAS) with running time <i>n</i><sup><i>O</i>(1/ε)</sup>, where <i>n</i> is the graph size and ε is the relative error allowed.When the planar graph has edge costs, we approximately solve the analogous min-cost subgraph problems in time <i>n… CONTINUE READING
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