由网友(满身坏脾气)分享简介:是否存在一个旅行商问题,其中的最佳解决方案具有跨的边缘? Does there exist a travelling salesman problem where the optimal solution has edges that cross? 的节点是在xy平面,所以交叉在这种情况下意味着,如果你要绘制的曲线...
是否存在一个旅行商问题,其中的最佳解决方案具有跨的边缘?
Does there exist a travelling salesman problem where the optimal solution has edges that cross?
的节点是在xy平面,所以交叉在这种情况下意味着,如果你要绘制的曲线图中,连接四个独立的节点都相交的两条线段
The nodes are in an x-y plane, so crossing in this case means if you were to draw the graph, two line segments connecting four separate nodes would intersect.
推荐答案
如果在一个封闭的折线横两条边,再有就是用相同的顶点的折线,但较小的周长。这是三角不等式的结果。因此,一个解决方案,以对TSP必须是一个简单的多边形。见这篇文章(图4)。
If two edges in a closed polygonal line cross, then there is a polygonal line with the same vertices but with smaller perimeter. This is a consequence of the triangle inequality. So, a solution to the TSP must be a simple polygon. See this article (Figure 4).
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