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
An efficient parameterized algorithm for m-set packing
Journal of Algorithms
Crown Structures for Vertex Cover Kernelization
Theory of Computing Systems
On Problems without Polynomial Kernels (Extended Abstract)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Faster Algebraic Algorithms for Path and Packing Problems
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
A faster parameterized algorithm for set packing
Information Processing Letters
Parameterized algorithms for weighted matching and packing problems
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses
Proceedings of the forty-second ACM symposium on Theory of computing
Linear kernels in linear time, or how to save k colors in O(n2) steps
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
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
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We present a reduction procedure that takes an arbitrary instance of the r-Set Packing problem and produces an equivalent instance whose number of elements is in O(k^r^-^1), where k is the input parameter. Such parameterized reductions are known as kernelization algorithms, and a reduced instance is called a problem kernel. Our result improves on previously known kernelizations by a factor of k. In particular, the number of elements in a 3-Set Packing kernel is improved from a cubic function of the parameter to a quadratic one.