Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Efficiently four-coloring planar graphs
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Fixed Parameter Algorithms for PLANAR DOMINATING SET and Related Problems
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Practical Algorithms on Partial k-Trees with an Application to Domination-like Problems
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Subexponential Parameterized Algorithms Collapse the W-Hierarchy
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Upper bounds for vertex cover further improved
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Improved Parameterized Algorithms for Planar Dominating Set
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Efficient Data Reduction for DOMINATING SET: A Linear Problem Kernel for the Planar Case
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
The Dominating Set Problem Is Fixed Parameter Tractable for Graphs of Bounded Genus
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Parameterized Complexity: The Main Ideas and Some Research Frontiers
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Improved Exact Algorithms for MAX-SAT
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Improved Tree Decomposition Based Algorithms for Domination-like Problems
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Graph Separators: A Parameterized View
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Graph Separator Algorithms: A Refined Analysis
WG '02 Revised Papers from the 28th 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
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
Algorithms and theory of computation handbook
Theory and application of width bounded geometric separators
Journal of Computer and System Sciences
Theory and application of width bounded geometric separator
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
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A parameterized problem is fixed parameter tractable if it admits a solving algorithm whose running time on input instance (I, k) is f(k)ċ|I|α, where f is an arbitrary function depending only on k. Typically, f is some exponential function, e.g., f(k) = ck for constant c. We describe general techniques to obtain growth of the form f(k) = ck for a large variety of planar graph problems. The key to this type of algorithm is what we call the "Layerwise Separation Property" of a planar graph problem. Problems having this property include PLANAR VERTEX COVER, PLANAR INDEPENDENT SET, AND PLANAR DOMINATING SET.