Primal-Dual Approximation Algorithms for Node-Weighted Network Design in Planar Graphs

Piotr Berman, Grigory Yaroslavtsev

Abstract: We present primal-dual algorithms which give a 2.4 approximation for a class of node-weighted network design problems in planar graphs, introduced by Demaine, Hajiaghayi and Klein (ICALP’09). This class includes Node-Weighted Steiner Forest problem studied recently by Moldenhauer (ICALP’11) and other node-weighted problems in planar graphs that can be expressed using (0,1)-proper functions introduced by Goemans and Williamson. We show that these problems can be equivalently formulated as feedback vertex set problems and analyze approximation factors guaranteed by different violation oracles within the primal-dual framework developed by Goemans and Williamson.