V2EX hamiltonian cycle

Hamiltonian Cycle

释义 Definition

哈密顿回路(哈密顿环):图论中的一种环路,指在一个图中存在一条闭合路径,恰好经过每个顶点一次并回到起点。(常见于组合数学与算法/复杂性理论;相关判定问题是经典难题。)

发音 Pronunciation (IPA)

/hml.t.ni.n sa.kl/

例句 Examples

A Hamiltonian cycle visits every vertex exactly once and returns to the start.
哈密顿回路会恰好访问每个顶点一次,并返回起点。

In many graphs, finding a Hamiltonian cycle is difficult, and the decision version is NP-complete.
在许多图中,寻找哈密顿回路很困难,而且其判定版本是 NP-完全的。

词源 Etymology

“Hamiltonian” 源自爱尔兰数学家 William Rowan Hamilton(威廉罗文哈密顿) 的姓氏;该术语用来纪念他与相关路径/循环思想的影响。与之对应的概念还有 Hamiltonian path(哈密顿路径)

相关词 Related Words

文学与经典著作中的出现 Literary Works

  • Douglas B. West, Introduction to Graph Theory(《图论导论》)
  • Reinhard Diestel, Graph Theory(《图论》)
  • Michael R. Garey & David S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness(《计算机与难解性》;讨论哈密顿回路问题的 NP-完全性)
  • Christos H. Papadimitriou, Computational Complexity(《计算复杂性》;以哈密顿回路作为经典复杂性例题)
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