Approximating minimum feedback vertex sets in hypergraphs

The feedback vertex set problem for hypergraphs is considered and an efficient approximation algorithm is presented. It is shown that an approximation factor of k is guaranteed when the cardinality of every hyperedge is bounded by an integer k, generalizing the existing result for ordinary graphs.

[1]  Piotr Berman,et al.  Constant Ratio Approximations of the Weighted Feedback Vertex Set Problem for Undirected Graphs , 1995, ISAAC.

[2]  John M. Lewis,et al.  The Node-Deletion Problem for Hereditary Properties is NP-Complete , 1980, J. Comput. Syst. Sci..

[3]  Dan Geiger,et al.  Approximation Algorithms for the Loop Cutset Problem , 1994, UAI.

[4]  Reuven Bar-Yehuda,et al.  A Local-Ratio Theorem for Approximating the Weighted Vertex Cover Problem , 1983, WG.

[5]  Raymond E. Miller,et al.  Complexity of Computer Computations , 1972 .

[6]  Toshihiro Fujito A Primal-Dual Approach to Approximation of Node-Deletion Problems for Matroidal Properties , 1997, ICALP.

[7]  Reuven Bar-Yehuda,et al.  Approximation algorithms for the vertex feedback set problem with applications to constraint satisfaction and Bayesian inference , 1994, SODA '94.

[8]  Randeep Bhatia,et al.  Book review: Approximation Algorithms for NP-hard Problems. Edited by Dorit S. Hochbaum (PWS, 1997) , 1998, SIGA.

[9]  Dorit S. Hochbaum,et al.  Approximation Algorithms for the Set Covering and Vertex Cover Problems , 1982, SIAM J. Comput..

[10]  P. Erd Os,et al.  On the maximal number of disjoint circuits of a graph , 2022, Publicationes Mathematicae Debrecen.

[11]  Burkhard Monien,et al.  Four Approximation Algorithms for the Feedback Vertex Set Problem , 1981, WG.

[12]  Carsten Lund,et al.  The Approximation of Maximum Subgraph Problems , 1993, ICALP.

[13]  Carsten Lund,et al.  Proof verification and hardness of approximation problems , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[14]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[15]  Mihalis Yannakakis,et al.  Optimization, approximation, and complexity classes , 1991, STOC '88.