V2EX tree decomposition

Tree Decomposition

释义 Definition

(图论/算法)树分解:把一个图按某种规则“拆成”一棵树状结构(由若干“袋子/子集”组成),使得图的边与顶点关系能在这棵树上被一致地表示。常用于定义与计算树宽(treewidth),并用来把一些在一般图上很难的问题,在“树状程度较高”的图上变得更容易求解。

例句 Examples

A tree decomposition can make some hard graph problems easier to solve.
树分解可以让一些困难的图问题更容易求解。

Using a tree decomposition of small width, we can run dynamic programming to compute the optimal solution efficiently.
利用一个宽度较小的树分解,我们可以用动态规划高效地计算最优解。

发音 Pronunciation

/tri dikmpozn/

词源 Etymology

tree 源自古英语 trēow / trēo(树、木材);decomposition 来自拉丁语构词:de-(分开、向下)+ componere(组合、放在一起)→ “拆开/分解”。作为图论术语,tree decomposition 在20世纪后期的算法图论中被系统化使用,尤其与 Robertson 与 Seymour 的图小子(Graph Minors)研究及“树宽”概念紧密相关。

相关词 Related Words

文学与著作 Literary Works

  • Graph Minors. II. Algorithmic aspects of tree-width Neil Robertson & P. D. Seymour(提出并系统讨论与树宽相关的树分解思想)
  • Graph Theory Reinhard Diestel(常用 “tree-decomposition(s)” 讲解树宽与结构理论)
  • Parameterized Algorithms Marek Cygan 等(将树分解作为参数化算法与动态规划的重要工具)
  • Algorithmic Graph Theory and Perfect Graphs Martin Charles Golumbic(在算法图论语境中涉及相关分解与结构方法)
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