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The NP-hard Multiple Hitting Set problem is finding a minimum-cardinality setintersecting each of the sets in a given input collection a given number oftimes. Generalizing a well-known data reduction algorithm due to Weihe, we showa problem kernel for Multiple Hitting Set parameterized by the Dilworth number,a graph parameter introduced by Foldes and Hammer in 1978 yet seemingly so farunexplored in the context of parameterized complexity theory. Using matrixmultiplication, we speed up the algorithm to quadratic sequential time andlogarithmic parallel time. We experimentally evaluate our algorithms. Byimplementing our algorithm on GPUs, we show the feasability of realizingkernelization algorithms on SIMD (Single Instruction, Multiple Date)architectures.

Serial and parallel kernelization of Multiple Hitting Set parameterized by the Dilworth number, implemented on the GPU