Quickest path queries on transportation network

Authors:
Radwa El Shawi;Joachim Gudmundsson;Christos Levcopoulos
Affiliations:
University of Sydney, Australia and NICTA, Australia;University of Sydney, Australia and NICTA, Australia;Lund University, Sweden
Venue:
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
Year:
2012

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Abstract

This paper considers the problem of finding a quickest path between two points in the Euclidean plane in the presence of a transportation network. A transportation network consists of a planar network where each road (edge) has an individual speed. A traveler may enter and exit the network at any point on the roads Along any road the traveler moves with a fixed speed depending on the road, and outside the network the traveler moves at unit speed in any direction. We give an exact algorithm for the basic version of the quickest path problem: given a transportation network with n edges in the Euclidean plane a source point s ε R2 and a destination point t ε R2, find the quickest path between s and t. We also show how the transportation network can be preprocessed in time O(n2 log n) into a data structure of size O(n2/ε2) such that (1 + ε)-approximate quickest path cost queries between any two points in the plane can be answered in time O(1/ε4 log n).