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

Given an undirected graph, finding either a minimum 2-edge-connected spanning subgraph or a minimum 2vertex-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/) , where n is the graph size and is the relative error allowed. When the planar graph has edge costs, we approximately solve the analogous min-cost subgraph problems in time nO(/) , where is the ratio of the total edge cost to the optimum solution cost.

• Type: Conference
• Year: 2004
• Where: SODA
• Authors: Artur Czumaj, Michelangelo Grigni, Papa Sissokho, Hairong Zhao
• Keywords: 2-edge-connected Spanning Subgraph, Algorithms, Planar Graph, SODA 2004, Spanning Subgraph