V2EX parameterized complexity

Parameterized Complexity

释义 / Definition

参数化复杂性:计算复杂性理论中的一个分支,用“参数”(如解的大小、树宽、图的度数等)来刻画问题难度。它关注:即使一个问题整体上很难(例如 NP-困难),当某个参数较小时,是否仍能设计高效算法(典型形式如运行时间为 \(f(k)\cdot n^{O(1)}\) 的算法)。

发音 / Pronunciation (IPA)

/prmtrazd kmplksti/

例句 / Examples

Parameterized complexity is useful for studying NP-hard problems.
参数化复杂性对于研究 NP-困难问题很有用。

In parameterized complexity, an algorithm can be efficient when the chosen parameter is small, even if the overall input size is large.
在参数化复杂性中,即使整体输入规模很大,只要选定的参数很小,算法也可能依然高效。

词源 / Etymology

“Parameterized”源自 parameter(参数),表示“用参数来描述/控制”;“complexity”表示“复杂性”。合起来指“用参数来刻画与分析计算问题复杂性的理论框架”。该术语在20世纪末随着固定参数可解(FPT)等概念的发展而广泛使用。

相关词 / Related Words

文献作品 / Notable Works

  • Rodney G. Downey & Michael R. Fellows,《Parameterized Complexity》(专著)
  • Marek Cygan, Fedor V. Fomin, ukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Micha Pilipczuk, Saket Saurabh,《Parameterized Algorithms》(专著)
  • **Marek Cygan et al.**,《Fundamentals of Parameterized Complexity》(教材/专著)
  • Rolf Niedermeier,《Invitation to Fixed-Parameter Algorithms》(专著,广泛讨论参数化复杂性相关思想)
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