Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Primal-Dual Approximation Algorithms for Feedback Problems
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs
Journal of the ACM (JACM)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Dominating Sets in Planar Graphs: Branch-Width and Exponential Speed-Up
SIAM Journal on Computing
Dynamic programming and fast matrix multiplication
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
New upper bounds on the decomposability of planar graphs
Journal of Graph Theory
On the Minimum Feedback Vertex Set Problem: Exact and Enumeration Algorithms
Algorithmica - Parameterized and Exact Algorithms
Randomized algorithms for the loop cutset problem
Journal of Artificial Intelligence Research
A cubic kernel for feedback vertex set
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Optimal branch-decomposition of planar graphs in O(n3) time
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
The undirected feedback vertex set problem has a poly(k) kernel
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Survey: Subexponential parameterized algorithms
Computer Science Review
On computing the minimum feedback vertex set of a directed graph by contraction operations
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Connecting face hitting sets in planar graphs
Information Processing Letters
Feedback vertex set on graphs of low clique-width
European Journal of Combinatorics
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The Planar Feedback Vertex Set problem asks, whether an n -vertex planar graph contains at most k vertices meeting all its cycles. The Face Cover problem asks, whether all vertices of a plane graph G lie on the boundary of at most k faces of G . Standard techniques from parameterized algorithm design indicate, that both problems can be solved by sub-exponential parameterized algorithms (where k is the parameter). In this paper, we improve the algorithmic analysis of both problems by proving a series of combinatorial results, relating the branchwidth of planar graphs with their face cover. Combining this fact with duality properties of branchwidth, allows us to derive analogous results on feedback vertex set. As a consequence, it follows that Planar Feedback Vertex Set and Face Cover can be solved in $O(2^{15.11\cdot \sqrt{k}}+ n^{O(1)})$ and $O(2^{10.1\cdot \sqrt{k}}+n^{O(1)})$ steps, respectively.