# Primal-Dual Approximation Algorithms for Feedback Problems in Planar Graphs

@article{Goemans1998PrimalDualAA,
title={Primal-Dual Approximation Algorithms for Feedback Problems in Planar Graphs},
author={Michel X. Goemans and David P. Williamson},
journal={Combinatorica},
year={1998},
volume={18},
pages={37-59}
}
• Published 1998
• Mathematics, Computer Science
• Combinatorica
A b s t r a c t . Given a subset of cycles of a graph, we consider the problem of finding a minimum-weight set of vertices that meets all cycles in the subset. This problem generalizes a number of problems, including the minlmum-weight feedback vertex set problem in both directed and undirected graphs, the subset feedback vertex set problem, and the graph bipartization problem~ in which one must remove a minimumweight set of vertices so that the remaining graph is bipartite. We give a…
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