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 $\mathrm{O}(k^d)$ 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.

中文翻译：

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线性时空中d命中集的最优大小问题核

已知的d-击键集线性时间内核化使用二次大小的数据结构（未完全初始化）确保线性最坏情况下的运行时间。摆脱这种数据结构，我们证明渐近最佳大小的问题内核$\mathrm{Ø}（{ķ}^d）$对于d-打击集，可以在线性时间和空间上进行计算。此外，我们在实验上比较了d-击键集的线性时间内核化和归因于Weihe的经典数据约简算法。