A Parameterized Perspective on Packing Paths of Length Two
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
A bounded search tree algorithm for parameterized face cover
Journal of Discrete Algorithms
A more effective linear kernelization for cluster editing
Theoretical Computer Science
A Problem Kernelization for Graph Packing
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
The parameterized complexity of the induced matching problem
Discrete Applied Mathematics
Linear kernelizations for restricted 3-Hitting Set problems
Information Processing Letters
On parameterized exponential time complexity
Theoretical Computer Science
On Parameterized Exponential Time Complexity
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Linear Kernel for Planar Connected Dominating Set
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of 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
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A linear kernel for a planar connected dominating set
Theoretical Computer Science
3-Hitting set on bounded degree hypergraphs: upper and lower bounds on the kernel size
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
An improved kernel for planar connected dominating set
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
A kernel of order 2k-clogk for vertex cover
Information Processing Letters
Journal of Combinatorial Optimization
Linear kernels for (connected) dominating set on H-minor-free graphs
Proceedings of the twenty-third 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
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
On the independence number of graphs with maximum degree 3
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Safe approximation and its relation to kernelization
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Simpler linear-time kernelization for planar dominating set
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Linear-Time computation of a linear problem kernel for dominating set on planar graphs
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Discrete Optimization
Kernels for packing and covering problems
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
What's next? future directions in parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
Kernel(s) for problems with no kernel: On out-trees with many leaves
ACM Transactions on Algorithms (TALG)
Polynomial kernels for dominating set in graphs of bounded degeneracy and beyond
ACM Transactions on Algorithms (TALG)
European Journal of Combinatorics
Nonblocker in h-minor free graphs: kernelization meets discharging
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
A 9k kernel for nonseparating independent set in planar graphs
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
On the independence number of graphs with maximum degree 3
Theoretical Computer Science
Note: Towards optimal kernel for connected vertex cover in planar graphs
Discrete Applied Mathematics
Improved linear problem kernel for planar connected dominating set
Theoretical Computer Science
A 9k kernel for nonseparating independent set in planar graphs
Theoretical Computer Science
Towards optimal kernel for edge-disjoint triangle packing
Information Processing Letters
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Determining whether a parameterized problem is kernelizable and has a small kernel size has recently become one of the most interesting topics of research in the area of parameterized complexity and algorithms. Theoretically, it has been proved that a parameterized problem is kernelizable if and only if it is fixed-parameter tractable. Practically, applying a data reduction algorithm to reduce an instance of a parameterized problem to an equivalent smaller instance (i.e., a kernel) has led to very efficient algorithms and now goes hand-in-hand with the design of practical algorithms for solving $\mathcal{NP}$-hard problems. Well-known examples of such parameterized problems include the vertex cover problem, which is kernelizable to a kernel of size bounded by $2k$, and the planar dominating set problem, which is kernelizable to a kernel of size bounded by $335k$. In this paper we develop new techniques to derive upper and lower bounds on the kernel size for certain parameterized problems. In terms of our lower bound results, we show, for example, that unless $\mathcal{P} = \mathcal{NP}$, planar vertex cover does not have a problem kernel of size smaller than $4k/3$, and planar independent set and planar dominating set do not have kernels of size smaller than $2k$. In terms of our upper bound results, we further reduce the upper bound on the kernel size for the planar dominating set problem to $67 k$, improving significantly the $335 k$ previous upper bound given by Alber, Fellows, and Niedermeier [J. ACM, 51 (2004), pp. 363-384]. This latter result is obtained by introducing a new set of reduction and coloring rules, which allows the derivation of nice combinatorial properties in the kernelized graph leading to a tighter bound on the size of the kernel. The paper also shows how this improved upper bound yields a simple and competitive algorithm for the planar dominating set problem.