V2EX path decomposition

Path Decomposition

释义 Definition

路径分解(Path Decomposition):图论中的一种表示方法,把一个图的顶点集合组织成按顺序排列的一串“袋(bags)”,使得每条边的两个端点会同时出现在某个袋中,并且每个顶点出现在这些袋中的位置必须形成一个连续区间。常用于定义与研究路径宽度(pathwidth)等结构参数。(该短语在一般语境下也可直译为“路径的分解/拆分”,但最常见的是图论义项。)

发音 Pronunciation (IPA)

/pθ dikmpozn/

例句 Examples

A path decomposition can help us analyze a graph step by step.
路径分解可以帮助我们一步一步地分析一个图。

Using a path decomposition of small width, the algorithm becomes more efficient on sparse graphs.
利用宽度较小的路径分解,该算法在稀疏图上会更高效。

词源 Etymology

path 来自古英语 p,意为“道路、路径”;decomposition 来自拉丁语系词根 *de-*(“向下、分开”)+ componere(“组合、构成”),引申为“分解”。在图论中,“path decomposition”强调用“像路径一样的线性顺序”来组织分解结构。

相关词 Related Words

文学与著作 Literary Works

  • Diestel, **Graph Theory**(多版教材中讨论树分解、路径分解及相关宽度参数)
  • Robertson & Seymour, Graph Minors 系列论文(图结构理论背景下与分解思想相关)
  • Bodlaender, “A Tourist Guide through Treewidth”(综述性文章中涉及路径/树分解与宽度概念)
  • Cygan et al., **Parameterized Algorithms**(参数化算法中常以分解为工具进行动态规划)
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