Nonconstructive tools for proving polynomial-time decidability
Journal of the ACM (JACM)
Efficient sets in partial k-trees
Discrete Applied Mathematics
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Face covers and the genus problem for Apex graphs
Journal of Combinatorial Theory Series B
Refined Search Tree Technique for DOMINATING SET on Planar Graphs
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Subexponential Parameterized Algorithms Collapse the W-Hierarchy
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Parameterized Complexity: Exponential Speed-Up for Planar Graph Problems
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Graph Separators: A Parameterized View
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Parameterized Complexity
Subexponential parameterized algorithms on graphs of bounded-genus and H-minor-free graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Parameterized complexity: exponential speed-up for planar graph problems
Journal of Algorithms
Bidimensionality: new connections between FPT algorithms and PTASs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs
ACM Transactions on Algorithms (TALG)
Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs
Journal of the ACM (JACM)
Improved bottleneck domination algorithms
Discrete Applied Mathematics
Planar Feedback Vertex Set and Face Cover: Combinatorial Bounds and Subexponential Algorithms
Graph-Theoretic Concepts in Computer Science
Fixed-parameter algorithms for the (k, r)-center in planar graphs and map graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
A linear kernel for planar feedback vertex set
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Kernel bounds for disjoint cycles and disjoint paths
Theoretical Computer Science
Fast sub-exponential algorithms and compactness in planar graphs
ESA'11 Proceedings of the 19th European conference on Algorithms
Approximate tree decompositions of planar graphs in linear time
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Information Processing Letters
Fast algorithms for hard graph problems: bidimensionality, minors, and local treewidth
GD'04 Proceedings of the 12th international conference on Graph Drawing
Algorithmic graph minor theory: improved grid minor bounds and wagner's contraction
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Simpler linear-time kernelization for planar dominating set
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Feedback vertex set on graphs of low clique-width
European Journal of Combinatorics
Approximate min-max relations on plane graphs
Journal of Combinatorial Optimization
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We present new fixed parameter algorithms for the FACE COVER problem on plane graphs. We show that if a plane graph has a face cover with at most k faces then its treewidth is bounded by O(驴k). An approximate tree decomposition can be obtained in linear time, and this is used to find an algorithm computing the face cover number in time O(c驴kn) for some constant c. Next we show that the problem is in linear time reducible to a problem kernel of O(k2) vertices, and this kernel can be used to obtain an algorithm that runs in time O(c驴k +n) for some other constant c. For the k-DISJOINT CYCLES PROBLEM AND THE k- FEEDBACK VERTEX SET problem on planar graphs we obtain algorithms that run in time O(c驴k log kn) for some constant c. For the k-FEEDBACK VERTEX SET problem we can further reduce the problem to a problem kernel of size O(k3) and obtain an algorithm that runs in time O(c驴k log k+n) for some constant c1.