V2EX treewidth

Treewidth

定义 Definition

treewidth(树宽)是图论与算法中的一个参数,用来衡量一个图在结构上“有多像一棵树”。树宽越小,图越接近树结构,很多原本困难的问题就更容易用树分解(tree decomposition)配合动态规划来高效求解。它也常用于参数化复杂性分析。

发音 Pronunciation (IPA)

/triwdθ/

例句 Examples

A tree has treewidth 1.
树的树宽是 1。

Many NP-hard problems become tractable on graphs of bounded treewidth using dynamic programming on a tree decomposition.
在树宽有界的图上,许多 NP-困难问题可以通过在树分解上做动态规划而变得可处理(高效可解)。

词源 Etymology

该词由 tree(树)+ width(宽度)构成,直译为“树的宽度”。它并不是指图的几何宽度,而是用“宽”来形象表达:当把图用树分解表示时,每个“袋(bag)”里需要容纳多少个顶点(更准确地说与袋大小相关),从而反映图偏离树结构的程度。

相关词 Related Words

文学与著作 Literary Works

  • Robertson, N. & Seymour, P. D. Graph Minors(系列论文,图小理论的重要来源;树宽与相关结构理论在其中占核心地位)
  • Diestel, R. Graph Theory(经典教材,讨论树分解、树宽及其与图结构的关系)
  • Cygan, M. et al. Parameterized Algorithms(参数化算法经典著作,大量使用树宽作为关键参数)
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