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Efficient Simplification: The (im)possibilities
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This was a tutorial about upper and lower bounds in kernelization back in 2010. While the upper bounds are mostly presented the same way, you might want to look up cross-composition for the lower bounds —while the ideas are similar, the terminology has evolved since. See the Kernelization book for a deep dive into both upper and lower bounds, and even coping strategies for lower bounds including Turing kernels and Lossy kernels.