Optimal construction of the city voronoi diagram

Authors:
Sang Won Bae;Jae-Hoon Kim;Kyung-Yong Chwa
Affiliations:
Div. of Computer Science, Dept. of EECS, Korea Advanced Institute of Science and Technology, Daejeon, Korea;Div. of Computer Engineering, Pusan University of Foreign Studies, Busan, Korea;Div. of Computer Science, Dept. of EECS, Korea Advanced Institute of Science and Technology, Daejeon, Korea
Venue:
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Year:
2006

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Abstract

We address proximity problems in the presence of roads on the L1 plane. More specifically, we present the first optimal algorithm for constructing the city Voronoi diagram. We apply the continuous Dijkstra paradigm to obtain an optimal algorithm for building a shortest path map for a given source, and then it extends to that for the city Voronoi diagram. Moreover, the algorithm applies to other generalized situations including metric spaces induced by roads and obstacles together.