Voronoi diagrams with a transportation network on the euclidean plane

Authors:
Sang Won Bae;Kyung-Yong Chwa
Affiliations:
Division of Computer Science, Department of EECS, Korea Advanced Institute of Science and Technology, Daejeon, Korea;Division of Computer Science, Department of EECS, Korea Advanced Institute of Science and Technology, Daejeon, Korea
Venue:
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Year:
2004

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Abstract

This paper investigates geometric and algorithmic properties of the Voronoi diagram with a transportation network on the Euclidean plane With a transportation network, the distance is measured as the length of the shortest (time) path In doing so, we introduce a needle, a generalized Voronoi site We present an O(nm2log n + m3log m) algorithm to compute the Voronoi diagram with a transportation network on the Euclidean plane, where n is the number of given sites and m is the complexity of the given transportation network.