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

Authors:
FabiáN A. Chudak;Michel X. Goemans;Dorit S. Hochbaum;David P. Williamson
Affiliations:
School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, USA;CORE, 34 Voie du Roman Pays, B-1348 Louvain-La-Neuve, Belgium;University of California, Department of IEOR, 4135 Etcheverry Hall, Berkeley, CA 94720, USA;IBM T.J. Watson Research Center, Room 33-219, P.O. Box 218, Yorktown Heights, NY 10598, USA
Venue:
Operations Research Letters
Year:
1998

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Abstract

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 well-known cycle formulation has an integrality gap of @Q(logn), as shown by Even, Naor, Schieber and Zosin. We also give a new 2-approximation algorithm for the problem which is a simplification of the Bafna et al. algorithm.