On the complexity of covering vertices by faces in a planar graph
SIAM Journal on Computing
A dynamic programming approach to the dominating set problem on k trees
SIAM Journal on Algebraic and Discrete Methods
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Graph classes: a survey
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Algorithms for Vertex Partitioning Problems on Partial k-Trees
SIAM Journal on Discrete Mathematics
Complexity of domination-type problems in graphs
Nordic Journal of 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
Parameterized Complexity: Exponential Speed-Up for Planar Graph Problems
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Vertex Cover: Further Observations and Further Improvements
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
Upper bounds for vertex cover further improved
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Parameterized Complexity
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
Exponential Speedup of Fixed-Parameter Algorithms on K3, 3-Minor-Free or K5-Minor-Free Graphs
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Approximation algorithms for classes of graphs excluding single-crossing graphs as minors
Journal of Computer and System Sciences
Tree-decompositions of small pathwidth
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Experimental evaluation of a tree decomposition-based algorithm for vertex cover on planar graphs
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Reducing to independent set structure: the case of k-internal spanning tree
Nordic Journal of Computing
Planar Branch Decompositions I: The Ratcatcher
INFORMS Journal on Computing
Dynamic programming and fast matrix multiplication
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
The Complexity Ecology of Parameters: An Illustration Using Bounded Max Leaf Number
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
The parameterized complexity of the induced matching problem
Discrete Applied Mathematics
Semi-nice tree-decompositions: The best of branchwidth, treewidth and pathwidth with one algorithm
Discrete Applied Mathematics
Tree-decompositions of small pathwidth
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Experimental evaluation of a tree decomposition-based algorithm for vertex cover on planar graphs
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Dynamic programming and planarity: Improved tree-decomposition based algorithms
Discrete Applied Mathematics
The parameterized complexity of the induced matching problem in planar graphs
FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
How to use planarity efficiently: new tree-decomposition based algorithms
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Problems parameterized by treewidth tractable in single exponential time: a logical approach
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Known algorithms on graphs of bounded treewidth are probably optimal
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Approximation algorithms for unit disk graphs
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Two birds with one stone: the best of branchwidth and treewidth with one algorithm
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Counting maximal independent sets in subcubic graphs
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Tree decompositions of graphs: Saving memory in dynamic programming
Discrete Optimization
Graph minors and parameterized algorithm design
The Multivariate Algorithmic Revolution and Beyond
Proceedings of the 2nd ACM SIGPLAN workshop on Functional high-performance computing
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We present an improved dynamic programming strategy for DOMINATING set and related problems on graphs that are given together with a tree decomposition of width k. We obtain an O(4kn) algorithm for dominating set, where n is the number of nodes of the tree decomposition. This result improves the previously best known algorithm of Telle and Proskurowski running in time O(9kn). The key to our result is an argument on a certain "monotonicity" in the table updating process during dynamic programming.Moreover, various other domination-like problems as discussed by Telle and Proskurowski are treated with our technique.We gain improvements on the base of the exponential term in the running time ranging between 55% and 68% in most of these cases. These results mean significant breakthroughs concerning practical implementations.