## Approximation Algorithms for the Feedback Vertex Set Problem with Applications to Constraint Satisfaction and Bayesian Inference (1998)

Citations: | 30 - 3 self |

### BibTeX

@MISC{Bar-Yehuda98approximationalgorithms,

author = {Reuven Bar-Yehuda and Dan Geiger and Joseph (Seffi) Naor and Ron M. Roth},

title = {Approximation Algorithms for the Feedback Vertex Set Problem with Applications to Constraint Satisfaction and Bayesian Inference},

year = {1998}

}

### Years of Citing Articles

### OpenURL

### Abstract

A feedback vertex set of an undirected graph is a subset of vertices that intersects with the vertex set of each cycle in the graph. Given an undirected graph G with n vertices and weights on its vertices, polynomial-time algorithms are provided for approximating the problem of finding a feedback vertex set of G with a smallest weight. When the weights of all vertices in G are equal, the performance ratio attained by these algorithms is 4 \Gamma (2=n). This improves a previous algorithm which achieved an approximation factor of O( p log n) for this case. For general vertex weights, the performance ratio becomes minf2\Delta 2 ; 4 log 2 ng where \Delta denotes the maximum degree in G. For the special case of planar graphs this ratio is reduced to 10. An interesting special case of weighted graphs where a performance ratio of 4 \Gamma (2=n) is achieved is the one where a prescribed subset of the vertices, so called blackout vertices, is not allowed to participate in any feedback verte...