A Quadratic Kernel for 3-Set Packing
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.
KeywordsFixed-parameter algorithms kernelization crown decomposition Set Packing
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- 2.Chor, B., Fellows, M.R., Juedes, D.: Linear Kernels in Linear Time, or How to Save k Colors in O(n 2) Steps. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds.) WG 2004. LNCS, vol. 3353, pp. 257–269. Springer, Heidelberg (2004)Google Scholar
- 3.Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, New York (1999)Google Scholar