具有独立对称权的极值组合结构的典型值

IF 0.7 4区数学 Q2 MATHEMATICS

Electronic Journal of Combinatorics Pub Date : 2022-11-22 DOI:10.37236/10237

Yun Cheng, Yixue Liu, T. Tkocz, Albert Xu

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引用次数: 3

摘要

假设一个完全图的边被随机独立地分配了权值，我们要求最小权值生成树的权值，或者说是完美匹配的权值，或者说是哈密顿循环的权值。对于这些和其他几个常见的优化问题，当权重是对称随机变量的独立副本(满足尾部概率的温和条件)时，我们建立了渐近紧界，特别是当权重是高斯的时候。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Typical Values of Extremal-Weight Combinatorial Structures with Independent Symmetric Weights

Suppose that the edges of a complete graph are assigned weights independently at random and we ask for the weight of the minimal-weight spanning tree, or perfect matching, or Hamiltonian cycle. For these and several other common optimisation problems, we establish asymptotically tight bounds when the weights are independent copies of a symmetric random variable (satisfying a mild condition on tail probabilities), in particular when the weights are Gaussian.

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来源期刊

Electronic Journal of Combinatorics 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

212

审稿时长

3-6 weeks

期刊介绍： The Electronic Journal of Combinatorics (E-JC) is a fully-refereed electronic journal with very high standards, publishing papers of substantial content and interest in all branches of discrete mathematics, including combinatorics, graph theory, and algorithms for combinatorial problems.