Optimal-size problem kernels for $d$-Hitting Set in linear time and space

René van Bevern; Pavel V. Smirnov

doi:10.1016/j.ipl.2020.105998

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arXiv · 2003.04578

Optimal-size problem kernels for $d$-Hitting Set in linear time and space

René van Bevern·Pavel V. Smirnov

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Abstract

The known linear-time kernelizations for $d$-Hitting Set guarantee linear worst-case running times using a quadratic-size data structure (that is not fully initialized). Getting rid of this data structure, we show that problem kernels of asymptotically optimal size $O(k^d)$ for $d$-Hitting Set are computable in linear time and space. Additionally, we experimentally compare the linear-time kernelizations for $d$-Hitting Set to each other and to a classical data reduction algorithm due to Weihe.

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René van Bevern, Pavel V. Smirnov. 2020-03-10. Optimal-size problem kernels for $d$-Hitting Set in linear time and space. https://doi.org/10.1016/j.ipl.2020.105998

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