V2EX matroid

Matroid

释义 Definition

拟阵(Matroid):组合数学中的一种抽象结构,用来概括“独立性/线性无关”这类概念(例如向量的线性无关、图中的无环边集)。它把“哪些子集算独立”用公理化方式描述,从而统一处理许多不同领域的“独立”问题。(该词基本是专业术语。)

发音 Pronunciation (IPA)

/metrd/

例句 Examples

A matroid captures the idea of independence.
拟阵用来刻画“独立性”这一概念。

Using a matroid model, we can justify why a greedy algorithm finds an optimal solution for certain selection problems.
借助拟阵模型,我们可以解释为什么贪心算法在某些选择类问题中能得到最优解。

词源 Etymology

matroidmatrix(矩阵) 的词根联想与后缀 -oid(……状/类似……的) 组合而来,表示“类似矩阵所体现的线性无关结构的东西”。该术语通常被认为源于 Hassler Whitney 在 20 世纪 30 年代对“线性依赖的抽象性质”的研究命名传统。

相关词 Related Words

文学与名著用例 Literary Works

  • Hassler Whitney, “On the Abstract Properties of Linear Dependence”(1935)提出并系统化拟阵思想的经典论文之一
  • James G. Oxley, Matroid Theory 拟阵理论的重要专著
  • D. J. A. Welsh, Matroid Theory 广为引用的拟阵教材/专著
  • Neil White (ed.), Theory of Matroids 拟阵领域的论文集/参考书
  • Alexander Schrijver, Combinatorial Optimization: Polyhedra and Efficiency 在组合优化背景下多次涉及拟阵与相关结构
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