V2EX big omega

Big Omega

Definition / 释义

Big Omega(大Ω记号,Ω)是算法与计算复杂度分析中的一种渐近下界表示法:若函数 \(f(n)\) 的增长速度在足够大的 \(n\) 上至少像 \(g(n)\) 那样快,则写作
\[ f(n) = \Omega(g(n)). \]
常用来表达“最少需要这么多时间/空间”。(在数学里 Ω 也可能有其他含义,但计算机科学中最常见的是“渐近下界”。)

Pronunciation / 发音(IPA)

/b ome/

Examples / 例句

For comparison-based sorting, the time complexity is Ω(n log n).
对于基于比较的排序算法,时间复杂度下界是 Ω(n log n)。

Although the average case may be faster, the algorithm still has an Ω(n) worst-case running time on adversarial inputs.
尽管平均情况可能更快,但在对抗性输入下,该算法的最坏运行时间仍然有 Ω(n) 的下界。

Etymology / 词源

“Big Omega”里的 Omega(Ω)来自希腊字母表的最后一个字母“ω/Ω”。在渐近符号体系中,它与 Big O(O)Big Theta(Θ)并列,形成一套用希腊字母表示增长(Landau 记号)的传统;其中 Ω被约定用来表示“从下方界定”的增长速度(下界)。

Related Words / 相关词汇

Literary Works / 文献与名著中的使用

  • Introduction to Algorithms(Cormen, Leiserson, Rivest, Stein),常用 Ω 记号讨论排序下界、递归式与渐近分析。
  • The Art of Computer Programming(Donald E. Knuth),在算法分析与渐近估计中系统使用 Landau 记号(含 Ω)。
  • Introduction to the Theory of Computation(Michael Sipser),在复杂度与可计算性相关章节中使用渐近符号讨论时间下界。
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