V2EX fixed-parameter tractable

Fixed-Parameter Tractable

释义 Definition

固定参数可解(固定参数可处理):在参数化复杂性理论中,指一个问题若能在时间 \(f(k)\cdot n^{O(1)}\) 内求解,则称其为固定参数可解(FPT)。其中 \(n\) 是输入规模,\(k\) 是选定的参数,\(f(k)\) 只依赖于参数而与 \(n\) 无关。常用于描述“当参数较小时时,尽管总体问题可能很难,仍可高效求解”。

发音 Pronunciation (IPA)

/fkst prmtr trktbl/

例句 Examples

This problem is fixed-parameter tractable when parameterized by solution size.
当以解的大小作为参数时,这个问题是固定参数可解的。

Although the general problem is NP-hard, it becomes fixed-parameter tractable on graphs of bounded treewidth.
虽然一般情形下该问题是 NP-困难的,但在树宽有界的图上它会变成固定参数可解。

词源 Etymology

该术语来自参数化算法(parameterized algorithms)参数化复杂性(parameterized complexity)领域:

  • fxed-parameter 表示“固定的参数 \(k\)”被单独拿出来影响复杂度;
  • tractable 意为“可处理、可在实践中有效求解”。
    合起来强调:复杂度允许对参数呈现较“昂贵”的依赖(如指数),但对输入规模 \(n\) 仍保持多项式级别,从而在参数较小时仍具有可行性。

相关词 Related Words

文学与著作中的用例 Literary / Notable Works

  • Rod G. Downey & Michael R. Fellows, Parameterized Complexity(1999)
  • Rolf Niedermeier, Invitation to Fixed-Parameter Algorithms(2006)
  • Marek Cygan, Fedor V. Fomin, ukasz Kowalik, et al., Parameterized Algorithms(2015)
  • J. Flum & M. Grohe, Parameterized Complexity Theory(2006)
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