论文标题
欧几里得旅行推销员问题与位置依赖和加权边缘
Euclidean traveling salesman problem with location dependent and power weighted edges
论文作者
论文摘要
考虑〜\（n \）节点〜\（\ {x_i \} _ {1 \ leq i \ leq n} \）在单位square〜 \（s，\）中独立分布，每个根据分布〜\ \（f \ \）和let〜 \（k_n \）每个图表均通过每个段组成nod nod nod nod nod nod nod nod nod nod nod。对于〜\（k_n \）中的每个边缘〜\（e \），我们将重量〜\（w（e）\）关联，该重量可能取决于〜\（e \）端动的\ emph {单个位置}（e \）的单个位置}，不一定是euclidean长度的力量，e。 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。\）
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~\(TSP_n.\)
