V2EX fixed-parameter tractability

Fixed-Parameter Tractability

定义 Definition

固定参数可解性/固定参数可处理性(FPT):参数化复杂性理论中的概念,指对输入规模为 n、参数为 k 的问题,若能在时间 f(k) n^O(1) 内求解(其中 f 只依赖于 k),则称该问题具有固定参数可解性。常用于说明:当参数 k 较小,即使 n 很大,问题仍可能“实际可做”。

发音 Pronunciation (IPA)

/fkst prmtr trktblti/

例句 Examples

Many graph problems become practical with fixed-parameter tractability.
许多图论问题在具有固定参数可解性时会变得更实用。

The paper proves fixed-parameter tractability by designing an algorithm that runs in f(k)n^3 time, where k is the size of the solution.
论文通过设计一个运行时间为 f(k)n^3 的算法证明了固定参数可解性,其中 k 是解的大小。

词源 Etymology

该术语由三部分组成:fixed-parameter(“固定参数的”)强调把某个结构性量(如解的大小、树宽等)作为参数 k 单独对待;tractability 来自 tractable(“可处理的、可解的”),源于拉丁语 tractare(“处理、操作”)。合起来表示:把“困难”主要限制在参数 k 上,而对输入规模 n 保持多项式级别的可处理性。

相关词 Related Words

文献作品 Literary & Notable Works

  • Parameterized Complexity Rod G. Downey & Michael R. Fellows
  • Parameterized Complexity Theory Jrg Flum & Martin Grohe
  • Invitation to Fixed-Parameter Algorithms Rolf Niedermeier
  • Parameterized Algorithms Marek Cygan, Fedor V. Fomin, ukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Micha Pilipczuk, Saket Saurabh
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