Catalan structures and dynamic programming in H-minor-free graphs
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Computational Study on Dominating Set Problem of Planar Graphs
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Planar Feedback Vertex Set and Face Cover: Combinatorial Bounds and Subexponential Algorithms
Graph-Theoretic Concepts in Computer Science
On parameterized exponential time complexity
Theoretical Computer Science
Computing branchwidth via efficient triangulations and blocks
Discrete Applied Mathematics
Semi-nice tree-decompositions: The best of branchwidth, treewidth and pathwidth with one algorithm
Discrete Applied Mathematics
On Parameterized Exponential Time Complexity
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Computational study on planar dominating set problem
Theoretical Computer Science
Computing branch decomposition of large planar graphs
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Capacitated domination and covering: a parameterized perspective
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Subexponential parameterized algorithms for degree-constrained subgraph problems on planar graphs
Journal of Discrete Algorithms
Improved induced matchings in sparse graphs
Discrete Applied Mathematics
Approximation algorithms for the capacitated domination problem
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Computational study for planar connected dominating set problem
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Note: On self-duality of branchwidth in graphs of bounded genus
Discrete Applied Mathematics
Fast sub-exponential algorithms and compactness in planar graphs
ESA'11 Proceedings of the 19th European conference on Algorithms
Dominating set is fixed parameter tractable in claw-free graphs
Theoretical Computer Science
Linear kernels for (connected) dominating set on H-minor-free graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
The complexity of two graph orientation problems
Discrete Applied Mathematics
Hybrid genetic algorithm for minimum dominating set problem
ICCSA'10 Proceedings of the 2010 international conference on Computational Science and Its Applications - Volume Part IV
A strengthened analysis of an algorithm for Dominating Set in planar graphs
Discrete Applied Mathematics
Algorithmic aspects of dominator colorings in graphs
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
Catalan structures and dynamic programming in H-minor-free graphs
Journal of Computer and System Sciences
Survey: Subexponential parameterized algorithms
Computer Science Review
Graph minors and parameterized algorithm design
The Multivariate Algorithmic Revolution and Beyond
Polynomial kernels for dominating set in graphs of bounded degeneracy and beyond
ACM Transactions on Algorithms (TALG)
Subexponential parameterized algorithms
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Dynamic programming for graphs on surfaces
ACM Transactions on Algorithms (TALG)
Beyond bidimensionality: Parameterized subexponential algorithms on directed graphs
Information and Computation
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We introduce a new approach to design parameterized algorithms on planar graphs which builds on the seminal results of Robertson and Seymour on graph minors. Graph minors provide a list of powerful theoretical results and tools. However, the widespread opinion in the graph algorithms community about this theory is that it is of mainly theoretical importance. In this paper we show how deep min-max and duality theorems from graph minors can be used to obtain exponential speed-up to many known practical algorithms for different domination problems. Our use of branch-width instead of the usual tree-width allows us to obtain much faster algorithms. By using this approach, we show that the k-dominating set problem on planar graphs can be solved in time O(215.13 \sqrt k + n3).