V2EX kernelization

Kernelization

定义 Definition

Kernelization(核化/核化预处理):在参数化复杂性(Parameterized Complexity)中,一种多项式时间的预处理方法,把输入实例 \((I, k)\) 通过规则化简为一个更小的等价实例 \((I', k')\),使其规模由仅依赖参数 \(k\) 的函数 \(f(k)\) 所界定(而与原始输入规模基本无关)。得到的小实例称为 kernel(核)
(在不同语境下也可能指“核函数化”等别的含义,但计算机科学中最常见的是上述算法意义。)

发音 Pronunciation (IPA)

/knlzen/

例句 Examples

Kernelization can shrink a hard problem instance before running an exact algorithm.
核化可以在运行精确算法之前先把困难问题的实例缩小。

By applying kernelization rules, the researchers reduced the graph to a kernel whose size depends only on the parameter \(k\), enabling faster downstream computation.
通过应用核化规则,研究人员把图缩减为一个大小只依赖参数 \(k\) 的核,从而加速了后续计算。

词源 Etymology

该词由 kernel(核、核心) + -ization(……化的过程) 构成。这里的 kernel 指“保留问题本质难点后的核心实例”,kernelization 就是“把问题化简到核心规模”的过程。作为参数化算法领域的术语,它随相关理论体系的发展而固定下来。

相关词 Related Words

文学与著作中的用例 Literary / Notable Works

  • Parameterized Complexity Rod G. Downey & Michael R. Fellows(系统讨论 kernelization 与核的概念与方法)
  • Parameterized Algorithms Marek Cygan, Fedor V. Fomin, ukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Micha Pilipczuk, Saket Saurabh(广泛使用并规范化介绍 kernelization 技术)
  • Kernelization: Theory of Parameterized Preprocessing Hans L. Bodlaender, Rodney G. Downey, Michael R. Fellows, Danny Hermelin(以 kernelization 为核心主题的研究综述/论述)
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