具有位置相关和权加权边的欧氏流动推销员问题
Euclidean traveling salesman problem with location dependent and power weighted edges
摘要：
考虑~ \(n\)节点~ \(\{X_i\}_{1 \leq i \leq n}\)根据分布~ \(f\)独立地分布在单位正方形~ \(S,\)中，并且令~ \(K_n\)是通过用直线段连接每对节点而形成的完全图。对于~ \(K_n\)中的每条边~ \(e\)，我们关联一个权重~ \(w(e)\)，该权重可以取决于~ \(e\)的端点的\emph{individual locations}，并且不一定是~ \(e.\)的欧几里德长度的幂。表示~ \(TSP_n\)是对应于旅行商问题（TSP）的~ \(K_n\)的生成环的最小权重，并且假设关于权重函数~ \(w(.),\)的等价条件，我们证明了~适当缩放和居中的\(TSP_n\)收敛到零a.s.\平均为~ \(n \rightarrow \infty.\)我们还得到了~ \(TSP_n.\)的上下界偏差估计
英文摘要：
Consider~\(n\) nodes~\(\{X_i\}_{1 \leq i \leq n}\) independently distributed in the unit square~\(S,\) each according to a distribution~\(f\) and let~\(K_n\) be the complete graph formed by joining each pair of nodes by a straight line segment. For every edge~\(e\) in~\(K_n\) we associate a weight~\(w(e)\) that may depend on the \emph{individual locations} of the endvertices of~\(e\) and is not necessarily a power of the Euclidean length of~\(e.\) Denoting~\(TSP_n\) to be the minimum weight of a spanning cycle of~\(K_n\) corresponding to the travelling salesman problem (TSP) and assuming an equivalence condition on the weight function~\(w(.),\) we prove that~\(TSP_n\) appropriately scaled and centred converges to zero a.s.\ and in mean as~\(n \rightarrow \infty.\) We also obtain upper and lower bound deviation estimates for~\(TSP_n.\)
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
