Linear Kernel for Planar Connected Dominating Set

Authors:
Daniel Lokshtanov;Matthias Mnich;Saket Saurabh
Affiliations:
Institutt for Informatikk, Universitetet i Bergen, Bergen, Norway 5020;Faculteit Wiskunde en Informatica, Technische Universiteit Eindhoven, Eindhoven, The Netherlands 5600 MB;Institutt for Informatikk, Universitetet i Bergen, Bergen, Norway 5020
Venue:
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Year:
2009

Citing 12
Cited 9

Vertex cover: further observations and further improvements

Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
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
Approximation Algorithms for Connected Dominating Sets

Algorithmica
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 Linear Kernel for the k-Disjoint Cycle Problem on Planar Graphs

ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
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
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

Bidimensionality and kernels

SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
An improved kernel for planar connected dominating set

TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
On parameterized independent feedback vertex set

COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Linear problem kernels for planar graph problems with small distance property

MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Parameterized complexity and inapproximability of dominating set problem in chordal and near chordal graphs

Journal of Combinatorial Optimization
Connectivity is not a limit for kernelization: planar connected dominating set

LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
On Parameterized Independent Feedback Vertex Set

Theoretical Computer Science
Planar graph vertex partition for linear problem kernels

Journal of Computer and System Sciences
Improved linear problem kernel for planar connected dominating set

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

We provide polynomial time data reduction rules for Connected Dominating Set in 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 to obtain linear kernels for other problems on planar graphs.