约束四点集的最短网络问题

SHORTEST NETWORK PROBLEM ON CONSTRAINED SETS OF FOUR POINTS

设Ｌ为Ｅｕｃｌｉｄｅａｎ平面上一连续曲线，在Ｌ的一侧有一个含ｎ个固定点的集合Ｎ，且点集Ｎ的凸包ＣＨ（Ｎ）与曲线Ｌ不相交．问题是在Ｌ上找一点ｐ，使点集Ｎ∪｛ｐ｝的互联网络最短．本文在Ｌ是圆及点集Ｎ含有３个点的条件下给出了问题解．

Let L be a continuous curve on Euclidean plane, N be a set of n fixed points on one side of L, and the convex hull of N, CH( N ), not touch the curve L. The problem is to find a point p on L such that the network interconnecting the set N∪{p} is the shortest.In this paper,the problem's answer is given under the condition that the N contains three points and the curve L is a circle.