February 2018
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86 Reads
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6 Citations
Theory of Computing Systems
We consider distance queries in vertex labeled planar graphs. For any fixed we show how to preprocess a planar graph with vertex labels and edge lengths into a data structure that answers queries of the following form. Given a vertex u and a label return a -approximation of the distance between u and its closest vertex with label . For an undirected n-vertex planar graph the preprocessing time is , the size is , and the query time is . For a directed planar graph with arc lengths bounded by N, the preprocessing time is , the data structure size is , and the query time is .