Vertex cover: further observations and further improvements
Journal of Algorithms
Polynomial-time data reduction for dominating set
Journal of the ACM (JACM)
Bidimensionality: new connections between FPT algorithms and PTASs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Parametric Duality and Kernelization: Lower Bounds and Upper Bounds on Kernel Size
SIAM Journal on Computing
Solving Connected Dominating Set Faster than 2 n
Algorithmica - Parameterized and Exact Algorithms
A quadratic kernel for feedback vertex set
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A Linear Kernel for the k-Disjoint Cycle Problem on Planar Graphs
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Parameterized and Exact Computation
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
The parameterized complexity of the induced matching problem in planar graphs
FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
A linear kernel for planar feedback vertex set
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Connectivity is not a limit for kernelization: planar connected dominating set
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Fixed-parameter tractability results for full-degree spanning tree and its dual
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Linear problem kernels for NP-hard problems on planar graphs
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Kernelization of packing problems
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Finding minimum weight connected dominating set in stochastic graph based on learning automata
Information Sciences: an International Journal
Improved linear problem kernel for planar connected dominating set
Theoretical Computer Science
Hi-index | 5.23 |
We provide polynomial time data reduction rules for Connected Dominating Set on planar graphs and analyze these to obtain a linear kernel for the planar Connected Dominating Set problem. To obtain the desired kernel we introduce a method that we call reduce or refine. Our kernelization algorithm analyzes the input graph and either finds an appropriate reduction rule that can be applied, or zooms in on a region of the graph which is more amenable to reduction. We find this method of independent interest and believe that it will be useful for obtaining linear kernels for other problems on planar graphs.