A primal–dual interpretation of two 2-approximation algorithms for the feedback vertex set problem in undirected graphs

Fabián A. Chudak, Michel X. Goemans, Dorit S. Hochbaum, David P. Williamson
1998 Operations Research Letters  
Recently, Becker and Geiger and Bafna, Berman and Fujito gave 2-approximation algorithms for the feedback vertex set problem in undirected graphs. We show how their algorithms can be explained in terms of the primal-dual method for approximation algorithms, which has been used to derive approximation algorithms for network design problems. In the process, we give a new integer programming formulation for the feedback vertex set problem whose integrality gap is at worst a factor of two; the
more » ... known cycle formulation has an integrality gap of (log n), as shown by Even, Naor, Schieber and Zosin. We also give a new 2-approximation algorithm for the problem which is a simpliÿcation of the Bafna et al. algorithm.
doi:10.1016/s0167-6377(98)00021-2 fatcat:lzekbcpn45eq3d5fysgrczumqe