We consider the following dynamic problem: given a fixed (small) template graph with colored vertices C and a large graph with colored vertices G (whose colors can be changed dynamically), how many mappings m are there from the vertices of C to vertices of G in such a way that the colors agree, and the distances between m(v) and m(w) have given values for every edge? We show that this problem can be solved efficiently on triangulations of the hyperbolic plane, as well as other Gromov hyperbolic graphs. For various template graphs C, this result lets us efficiently solve various computational problems which are relevant in applications, such as visualization of hierarchical data and social network analysis.

翻译：我们考虑以下动态问题:给定一个带有彩色脊椎C的固定(小)模板图和一个带有彩色脊椎G(其颜色可以动态地改变)的大图,从C的脊椎到G的脊椎有多少映射 m,其颜色一致,以及m(v)和m(w)之间的距离给每个边缘提供了值。我们显示,在双曲线的三角图和其他格罗莫夫双曲线图上,这个问题可以有效解决。对于各种模板图C,这一结果使我们能够有效地解决与应用程序有关的各种计算问题,例如等级数据和社会网络分析的可视化。