An improved kernelization algorithm for r-Set Packing - Abu-Khzam, Faisal N. (Information processing letters, 2010)
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.