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Efficient Dynamic Approximate Distance Oracles for Vertex-Labeled Planar Graphs
Theory of Computing Systems ( IF 0.6 ) Pub Date : 2019-09-11 , DOI: 10.1007/s00224-019-09949-5
Itay Laish , Shay Mozes

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:

顶点标签平面图的有效动态近似距离Oracle

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λģ。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。
更新日期:2019-09-11
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