V2EX bikernelization

Bikernelization

定义 Definition

bikernelization(双核化):参数化复杂性理论中的一种预处理(数据约简)方法,把一个参数化问题实例 \((I, k)\) 在多项式时间内转换为可能属于另一个问题的实例 \((I', k')\),使其与原实例等价(通常指可相互推出“是/否”答案),并且输出规模用参数的函数 \(f(k)\) 进行上界约束。
常见对比:kernelization 通常把问题约简到“同一个问题”的小实例;bikernelization 允许约简到“不同但相关的问题”。

发音 Pronunciation (IPA)

/bak.n.laze.n/

例句 Examples

Bikernelization can reduce a huge instance to a much smaller one using the parameter.
双核化可以利用参数,把一个很大的实例约简成更小的实例。

In parameterized algorithms, a polynomial-time bikernelization may map one problem to a different but equivalent problem while guaranteeing the reduced instance size is bounded by a function of \(k\).
在参数化算法中,多项式时间的双核化可以把一个问题映射到另一个不同但等价的问题,同时保证约简后实例的大小由 \(k\) 的某个函数所界定。

词源 Etymology

**bi-**(“两/双”,表示涉及两个问题或两类实例)+ kernel(“核”,指约简后的核心小实例)+ -ization(名词后缀,表示“过程/化”)构成。该术语主要出现在参数化复杂性与内核化预处理的研究语境中。

相关词 Related Words

文献作品 Literary / Notable Works

  • Hans L. Bodlaender, Rodney G. Downey, Michael R. Fellows, Danny Hermelin. On Problems Without Polynomial Kernels(2009)
  • Hans L. Bodlaender, Bart M. P. Jansen, Stefan Kratsch. Kernelization: Theory of Parameterized Preprocessing(专著/综述性质作品,系统讨论 kernelization 与相关概念,常涉及 bikernelization 的位置与用途)
  • J. Flum, M. Grohe. Parameterized Complexity Theory(2006,参数化复杂性经典教材,讨论内核化等基础工具;相关章节常被用来引出 bikernelization 等扩展概念)
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