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
Faster Fixed-Parameter Tractable Algorithms for Matching and Packing Problems
Algorithmica - Parameterized and Exact Algorithms
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
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
Parameterized Complexity
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We present a reduction procedure that takes an arbitrary instance of the 3-Set Packing problem and produces an equivalent instance whose number of elements is bounded by a quadratic function of the input parameter. Such parameterized reductions are known as kernelization algorithms, and each reduced instance is called a problem kernel. Our result improves on previously known kernelizations and can be generalized to produce improved kernels for the r -Set Packing problem whenever r is a fixed constant. Improved kernelization for r -Dimensional-Matching can also be inferred.