Let G be a graph where each vertex is associated with a label. A vertex-labeled approximate distance oracle is a data structure that, given a vertex v and a label λ, returns a (1 + ε)-approximation of the distance from v to the closest vertex with label λ in G. Such an oracle is dynamic if it also supports label changes. In this paper we present three different dynamic approximate vertex-labeled distance oracles for planar graphs, all with polylogarithmic query and update times, and nearly linear space requirements. No such oracles were previously known.

中文翻译：

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顶点标签平面图的有效动态近似距离Oracle

令G为每个顶点与标签关联的图形。甲顶点标记的近似距离的Oracle是一种数据结构，给定一个顶点v和标签λ，返回一个（1 + ε从）的距离-近似v与标签最接近顶点λ在ģ。如果该预言还支持标签更改，则它是动态的。在本文中，我们为平面图提供了三种不同的动态近似顶点标记距离预言，它们均具有对数查询和更新时间，并且几乎具有线性空间要求。以前没有这样的预言。