The NP-completeness of Steiner Tree and Dominating Set for chordal bipartite graphs
Theoretical Computer Science
On the complexity of covering vertices by faces in a planar graph
SIAM Journal on Computing
Dominating sets in perfect graphs
Discrete Mathematics - Topics on domination
Handbook of theoretical computer science (vol. A)
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Efficient Algorithms for the Domination Problems on Interval and Circular-Arc Graphs
SIAM Journal on Computing
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Graph classes: a survey
A (2 + &egr;)-approximation scheme for minimum domination on circle graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
Independent Sets in Asteroidal Triple-Free Graphs
ICALP '97 Proceedings of the 24th 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
Parameterized Complexity
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
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,
On Efficient Fixed Parameter Algorithms for WEIGHTED VERTEX COVER
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
Faster Fixed Parameter Tractable Algorithms for Undirected Feedback Vertex Set
ISAAC '02 Proceedings of the 13th 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
-Approximation for Treewidth of Graphs Excluding a Graph with One Crossing as a Minor
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
An exact algorithm for connected red-blue dominating set
Journal of Discrete Algorithms
Parameterized problems on coincidence graphs
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
An exact algorithm for connected red-blue dominating set
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Survey: Subexponential parameterized algorithms
Computer Science Review
Subexponential parameterized algorithms
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
| Hi-index | 0.00 |
We present an algorithm for computing the domination number of a planar graph that uses O(c√kn) time, where k is the domination number of the given planar input graph and c = 36√34. To obtain this result, we show that the treewidth of a planar graph with domination number k is O(√k), and that such a tree decomposition can be found in O(√kn) time. The same technique can be used to show that the DISK DIMENSION problem (find a minimum set of faces that cover all vertices of a given plane graph) can be solved in O(c1√k n) time for c1 = 26√34. Similar results can be obtained for some variants of DOMINATING SET, e.g., INDEPENDENT DOMINATING SET.