V2EX cross-composition

Cross-composition

释义 Definition

交叉合成(cross-composition):计算复杂性理论(尤其是参数化复杂性与核化 kernelization)中的一种证明技术,用来把多个同类输入实例在多项式时间内“合成”为一个参数化实例,从而用于证明某些问题不太可能存在多项式核(polynomial kernel),除非出现被广泛认为不成立的复杂性塌缩(如 NP coNP/poly)。

发音 Pronunciation (IPA)

/krs kmpzn/
/krs kmpzn/

例句 Examples

Cross-composition is used to show that this problem likely has no polynomial kernel.
交叉合成常用于说明这个问题很可能不存在多项式核。

By designing a cross-composition from many SAT instances into a single parameterized instance, the authors derive a kernelization lower bound under standard complexity assumptions.
通过把多个 SAT 实例交叉合成为一个参数化实例,作者在常见的复杂性假设下推出了核化下界。

词源 Etymology

由 **cross-**(“交叉的、跨越多个的”)与 composition(“合成、组合”)构成,字面含义是“跨多个入的合成”。在参数化复杂性语境中,它特指把许多实例“交叉”地编码进一个实例的构造方法。

相关词 Related Words

文献作品 Literary Works

  • Bodlaender, Jansen, Kratsch, Cross-Composition: A New Technique for Kernelization Lower Bounds(提出并系统化该技术的代表性论文)
  • Cygan et al., Parameterized Algorithms(参数化算法教材中对核化下界与相关技术的讨论)
  • Downey & Fellows, Parameterized Complexity(参数化复杂性经典著作中关于核化与下界方法的相关脉络)
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