Weak Kernels

In this paper, we formalize a folklore concept and formally d efineweak kernelsfor (NPhard) search problems, which is about search space reductio n and stands as a new generic technique for designing FPT algorithms. We show that weak ke rnels are different from the (traditional) kernels for decision problems, by exhibitin g an example out of P such that its decision version has no kernel while the equivalent search p oblem has a weak kernel. We show a few applications of weak kernels, for which a traditio nal kernelization seems hard to apply. Among them, we present the first FPT algorithm for the f amous Sorting by Minimum Unsigned Reversals problem. Department of Computer Science, Montana State University, Bozeman, MT 59717, USA. Email: htjiang@cs.montana.edu. Department of Computer Science, Shanghai Jiao Tong Univers ity, Shanghai 200030, China. Email: chihao.zhang@gmail.com. Corresponding author. Department of Computer Science, Mon tana State University, Bozeman, MT 59717, USA. Email: bhz@cs.montana.edu.

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