ACM Transactions on Mathematical Software (TOMS)
New bounds on the size of the minimum feedback vertex set in meshes and butterflies
Information Processing Letters
Combinatorial algorithms for feedback problems in directed graphs
Information Processing Letters
Minimum feedback vertex sets in shuffle-based interconnection networks
Information Processing Letters
New upper bounds on feedback vertex numbers in butterflies
Information Processing Letters
Local ratio: A unified framework for approximation algorithms. In Memoriam: Shimon Even 1935-2004
ACM Computing Surveys (CSUR)
Faster fixed parameter tractable algorithms for finding feedback vertex sets
ACM Transactions on Algorithms (TALG)
Exact computation of minimum feedback vertex sets with relational algebra
Fundamenta Informaticae
Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization
Journal of Computer and System Sciences
Feedback vertex sets in mesh-based networks
Theoretical Computer Science
An efficient algorithm for minimum feedback vertex sets in rotator graphs
Information Processing Letters
Feedback numbers of de Bruijn digraphs
Computers & Mathematics with Applications
Two hardness results on feedback vertex sets
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Tractable feedback vertex sets in restricted bipartite graphs
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
A Tabu search heuristic based on k-diamonds for the weighted feedback vertex set problem
INOC'11 Proceedings of the 5th international conference on Network optimization
Bidimensionality and geometric graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
The generalized deadlock resolution problem
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
An O(2O(k)n3) FPT algorithm for the undirected feedback vertex set problem*
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Improved fixed-parameter algorithms for two feedback set problems
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Hitting diamonds and growing cacti
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Safe approximation and its relation to kernelization
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Fixed-parameter tractability for the subset feedback set problem and the S-cycle packing problem
Journal of Combinatorial Theory Series B
Exact Computation of Minimum Feedback Vertex Sets with Relational Algebra
Fundamenta Informaticae
Feedback vertex set on graphs of low clique-width
European Journal of Combinatorics
Feedback vertex sets on restricted bipartite graphs
Theoretical Computer Science
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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 smallest weight. When the weights of all vertices in G are equal, the performance ratio attained by these algorithms is 4-(2/n). This improves a previous algorithm which achieved an approximation factor of $O(\sqrt{\log n})$ for this case. For general vertex weights, the performance ratio becomes $\min\{2\Delta^2, 4 \log_2 n\}$ 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-(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 vertex set.It is shown how these algorithms can improve the search performance for constraint satisfaction problems. An application in the area of Bayesian inference of graphs with blackout vertices is also presented.