自逼近图
Self-Approaching Graphs
摘要：
在本文中，我们介绍了自逼近图绘图。一个图的直线图是自逼近的，如果对于任何原点s和任何终点t，图中存在st-路，使得对于路径上的任何点q，当点p沿着从原点到q的路径连续移动时，从p到q的欧氏距离总是减小。这是一个比贪婪绘图（仅路径上的顶点与目标顶点之间的距离必须减小）更严格的条件，并保证绘图是5.33-n。我们研究三个主题：（1）识别自逼近图;（2）构造给定图的自逼近图;（3）构造连接给定点集的自逼近Steiner网络。我们证明：（1）在R^2和R^3中有有效的算法来检验多边形路径是否是自逼近的，但检验R^3中给定的图是否有自逼近的uv路径是NP难的;（2）我们可以刻画有自逼近图的树;（3）对于平面上任意给定的端点集，我们可以找到一个线性规模的网络，该网络在任意有序的端点对之间具有自逼近路径。
英文摘要：
In this paper we introduce self-approaching graph drawings. A straight-line drawing of a graph is self-approaching if, for any origin vertex s and any destination vertex t, there is an st-path in the graph such that, for any point q on the path, as a point p moves continuously along the path from the origin to q, the Euclidean distance from p to q is always decreasing. This is a more stringent condition than a greedy drawing (where only the distance between vertices on the path and the destination vertex must decrease), and guarantees that the drawing is a 5.33-spanner. We study three topics: (1) recognizing self-approaching drawings; (2) constructing self-approaching drawings of a given graph; (3) constructing a self-approaching Steiner network connecting a given set of points. We show that: (1) there are efficient algorithms to test if a polygonal path is self-approaching in R^2 and R^3, but it is NP-hard to test if a given graph drawing in R^3 has a self-approaching uv-path; (2) we can characterize the trees that have self-approaching drawings; (3) for any given set of terminal points in the plane, we can find a linear sized network that has a self-approaching path between any ordered pair of terminals.
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。
