Linear Programming Based Approximation Algorithms for Feedback Set Problems in Bipartite Tournaments
We consider the feedback vertex set and feedback arc set problems in bipartite tournaments. We improve on recent results by giving a 2-approximation algorithm for the feedback vertex set problem. We show that this result is the best we can attain when using a certain linear program as the lower bound on the optimal value. For the feedback arc set problem in bipartite tournaments, we show that a recent 4-approximation algorithm proposed by Gupta [5,6] is incorrect. We give an alternative 4-approximation algorithm based on an algorithm for feedback arc set in (regular) tournaments in [10,11].
KeywordsRecursive Call Linear Program Relaxation Complementary Slackness Feasible Integer Solution Improve Approximation Algorithm
Unable to display preview. Download preview PDF.
- 1.Ailon, N., Charikar, M., Newman, A.: Aggregating inconsistent information: ranking and clustering. In: STOC 2005: Proceedings of the 37th Annual ACM Symposium on Theory of Computing, pp. 684–693 (2005)Google Scholar
- 7.Kann, V.: On the approximability of NP-complete optimization problems, Ph.D. thesis, Department of Numerical Analysis and Computing Science, Royal Institute of Technology, Stockholm (1992)Google Scholar
- 10.van Zuylen, A., Hegde, R., Jain, K., Williamson, D.P.: Deterministic pivoting algorithms for constrained ranking and clustering problems. In: SODA 2007: Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 405–414 (2007)Google Scholar
- 11.van Zuylen, A., Williamson, D.P.: Deterministic pivoting algorithms for constrained ranking and clustering problems. Math. Oper. Res. (to appear), http://www.itcs.tsinghua.edu.cn/~anke/MOR.pdf