Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
Three partition refinement algorithms
SIAM Journal on Computing
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
A 2-Approximation Algorithm for the Undirected Feedback Vertex Set Problem
SIAM Journal on Discrete Mathematics
Approximating Minimum Subset Feedback Sets in Undirected Graphs with Applications
SIAM Journal on Discrete Mathematics
Wavelength conversion in optical networks
Journal of Algorithms
How to Solve NP-hard Graph Problems on Clique-Width Bounded Graphs in Polynomial Time
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
Faster fixed parameter tractable algorithms for finding feedback vertex sets
ACM Transactions on Algorithms (TALG)
Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization
Journal of Computer and System Sciences
Finding Branch-Decompositions and Rank-Decompositions
SIAM Journal on Computing
On the Minimum Feedback Vertex Set Problem: Exact and Enumeration Algorithms
Algorithmica - Parameterized and Exact Algorithms
Planar Feedback Vertex Set and Face Cover: Combinatorial Bounds and Subexponential Algorithms
Graph-Theoretic Concepts in Computer Science
Feedback Vertex Set on Graphs of Low Cliquewidth
Combinatorial Algorithms
On parse trees and Myhill-Nerode-type tools for handling graphs of bounded rank-width
Discrete Applied Mathematics
H-join decomposable graphs and algorithms with runtime single exponential in rankwidth
Discrete Applied Mathematics
Solving Connectivity Problems Parameterized by Treewidth in Single Exponential Time
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
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 algorithms for the feedback vertex set problems
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
On the recognition of k-equistable graphs
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
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The Feedback Vertex Set problem asks whether a graph contains q vertices meeting all its cycles. This is not a local property, in the sense that we cannot check if q vertices meet all cycles by looking only at their neighbors. Dynamic programming algorithms for problems based on non-local properties are usually more complicated. In this paper, given a graph G of clique-width cw and a cw-expression of G, we solve the Minimum Feedback Vertex Set problem in time O(n^22^O^(^c^w^l^o^g^c^w^)). Our algorithm applies dynamic programming on a so-called k-module decomposition of a graph, as defined by Rao (2008) [29], which is easily derivable from ak-expression of the graph. The related notion of module-width of a graph is tightly linked to both clique-width and NLC-width, and in this paper we give an alternative equivalent characterization of module-width.