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

Authors:
Artur Czumaj;Michelangelo Grigni;Papa Sissokho;Hairong Zhao
Affiliations:
New Jersey Institute of Technology, Newark, NJ;Emory University, Atlanta, GA;Illinois State University, Normal, IL;New Jersey Institute of Technology, Newark, NJ
Venue:
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2004

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Abstract

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 nO(1/ε), where n 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 nO(γ/ε), where γ is the ratio of the total edge cost to the optimum solution cost.