Abstract
We consider the following NP-hard problem: in a weighted graph, find a minimum cost set of vertices whose removal leaves a graph in which no two cycles share an edge. We obtain a constant-factor approximation algorithm, based on the primal-dual method. Moreover, we show that the integrality gap of the natural LP relaxation of the problem is Θ(logn), where n denotes the number of vertices in the graph.
This work was supported by the “Actions de Recherche Concertées” (ARC) fund of the “Communauté française de Belgique”.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Bafna, V., Berman, P., Fujito, T.: A 2-approximation algorithm for the undirected feedback vertex set problem. SIAM Journal on Discrete Mathematics 12(3), 289–297 (1999)
Bar-Yehuda, R., Geiger, D., Naor, J., Roth, R.M.: Approximation algorithms for the feedback vertex set problem with applications to constraint satisfaction and Bayesian inference. SIAM Journal on Computing 27(4), 942–959 (1998)
Becker, A., Geiger, D.: Optimization of Pearl’s method of conditioning and greedy-like approximation algorithms for the vertex feedback set problem. Artificial Intelligence 83, 167–188 (1996)
Chudak, F.A., Goemans, M.X., Hochbaum, D.S., Williamson, D.P.: A primaldual interpretation of two 2-approximation algorithms for the feedback vertex set problem in undirected graphs. Operations Research Letters 22, 111–118 (1998)
Even, G., Naor, J., Schieber, B., Zosin, L.: Approximating minimum subset feedback sets in undirected graphs with applications. SIAM Journal on Discrete Mathematics 13(2), 255–267 (2000)
Fiorini, S., Joret, G., Pietropaoli, U.: Hitting diamonds and growing cacti (2010), http://arxiv.org/abs/0911.4366v2
Goemans, M.X., Williamson, D.P.: The primal-dual method for approximation algorithms and its application to network design problems. In: Approximation Algorithms for NP-Hard Problems, ch. 4, pp. 144–191. PWS Publishing Company (1997)
Khot, S., Regev, O.: Vertex cover might be hard to approximate to within 2 − ε. Journal of Computer and System Sciences 74(3), 334–349 (2008)
Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Prentice-Hall, Englewood Cliffs (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fiorini, S., Joret, G., Pietropaoli, U. (2010). Hitting Diamonds and Growing Cacti. In: Eisenbrand, F., Shepherd, F.B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2010. Lecture Notes in Computer Science, vol 6080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13036-6_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-13036-6_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13035-9
Online ISBN: 978-3-642-13036-6
eBook Packages: Computer ScienceComputer Science (R0)