Efficient Dynamic Approximate Distance Oracles for Vertex-Labeled Planar Graphs
نویسندگان
چکیده
منابع مشابه
Distance Oracles for Vertex-Labeled Graphs
Given a graph G = (V,E) with non-negative edge lengths whose vertices are assigned a label from L = {λ1, . . . , λl}, we construct a compact distance oracle that answers queries of the form: “What is δ(v, λ)?”, where v ∈ V is a vertex in the graph, λ ∈ L a vertex label, and δ(v, λ) is the distance (length of a shortest path) between v and the closest vertex labeled λ in G. We formalize this nat...
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Consider an undirected weighted graph G = (V,E) with |V | = n and |E| = m, where each vertex v ∈ V is assigned a label from a set of labels L = {λ1, ..., λl}. We show how to construct a compact distance oracle that can answer queries of the form: “what is the distance from v to the closest λ-labeled node” for a given node v ∈ V and label λ ∈ L. This problem was introduced by Hermelin, Levy, Wei...
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We present an algorithm that computes a (1 + ε)-approximation of the diameter of a weighted, undirected planar graph of n vertices with non-negative edge lengths inO ( n logn ( logn+ (1/ε)5 )) expected time, improving upon the O ( n ( (1/ε)4 log4 n+ 2O(1/ε) )) -time algorithm of Weimann and Yuster [ICALP 2013]. Our algorithm makes two improvements over that result: first and foremost, it replac...
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A fundamental operation over edge-labeled graphs is the computation of shortest-path distances subject to a constraint on the set of permissible edge labels. Applying exact algorithms for such an operation is not a viable option, especially for massive graphs, or in scenarios where the distance computation is used as a primitive for more complex computations. In this paper we study the problem ...
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ژورنال
عنوان ژورنال: Theory of Computing Systems
سال: 2019
ISSN: 1432-4350,1433-0490
DOI: 10.1007/s00224-019-09949-5