V2EX w-hierarchy

W-hierarchy

Definition / 定义

W-hierarchy(W 层级):参数化复杂性理论中的一个分层体系,用来按“难度层次”分类一些固定参数不可解(通常被认为不太可能有高效参数算法)的参数化问题,常见层级包括 W[1]、W[2]、…。它用于与 FPT(固定参数可解) 等类别对比,帮助判断某个参数化问题是否可能存在高效算法。

Pronunciation / 发音(IPA)

/dbl.ju harrki/

Examples / 例句

The problem is believed to be in the W-hierarchy.
这个问题被认为属于 W 层级中的某一类。

By designing a parameterized reduction, the authors place the task within the W-hierarchy of parameterized complexity.
通过构造参数化归约,作者将该任务定位到参数化复杂性中的 W 层级之内。

Etymology / 词源

这里的 W 源自参数化复杂性中对布尔电路结构的刻画(常与电路的“weft(纬度)/结构层次”这类概念相关),W-hierarchy 这一框架在 1990 年代由 Rod DowneyMichael Fellows 等学者系统化,用来把许多经典的组合问题按参数化难度分层整理(如 W[1]-hard、W[2]-complete 等)。

Related Words / 相关词

Notable Works / 文献作品中的出现

  • Parameterized Complexity(Downey & Fellows, 1999)
  • Fundamentals of Parameterized Complexity(Cygan, Fomin, Kowalik, Lokshtanov, Marx, Pilipczuk, Pilipczuk, Saurabh, 2015)
  • Flum & Grohe 的参数化复杂性相关著作与综述中也会系统讨论 W-hierarchy(如 W[1]、W[2] 及其完备性结果)
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