拓扑和路由问题：循环框架
Topology and Routing Problems: The Circular Frame
摘要：
在这项工作中，我们解决了问题的不相交的路径之间的平面上的一个新的方法，借用的思想，从几何拓扑学，特别是从研究的多边形模式在数学。我们使用拓扑变换的2维平面布线环境，简化了布线问题成一个问题的连接点的圆与直线段，不相交的内部的圆。这些点或者是需要通过非相交路径连接的点，或者是在变换之前将原始环境的拓扑参数化的特殊“参考”点。当圆上所有必要的点都完全连接时，将反转变换，使线段组合成为连接原始环境中起点和终点的不相交路径。我们解释了转换后的环境中，路由问题的解决作为一个新的数据结构，任何路由问题都可以有效地解决。我们进行了实验，并表明新的路由算法的路由时间和成功率优于A* 算法。
英文摘要：
In this work, we solve the problem of finding non-intersecting paths between points on a plane with a new approach by borrowing ideas from geometric topology, in particular, from the study of polygonal schema in mathematics. We use a topological transformation on the 2-dimensional planar routing environment that simplifies the routing problem into a problem of connecting points on a circle with straight line segments that do not intersect in the interior of the circle. These points are either the points that need to be connected by non-intersecting paths or special `reference' points that parametrize the topology of the original environment prior to the transformation. When all the necessary points on the circle are fully connected, the transformation is reversed such that the line segments combine to become the non-intersecting paths that connect the start and end points in the original environment. We interpret the transformed environment in which the routing problem is solved as a new data structure where any routing problem can be solved efficiently. We perform experiments and show that the routing time and success rate of the new routing algorithm outperforms the ones for the A*-algorithm.
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