Linear time algorithms for visibility and shortest path problems inside simple polygons
SCG '86 Proceedings of the second annual symposium on Computational geometry
An incremental algorithm for a generalization of the shortest-path problem
Journal of Algorithms
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Two-Dimensional Voronoi Diagrams in the Lp-Metric
Journal of the ACM (JACM)
Dog Bites Postman: Point Location in the Moving Voronoi Diagram and Related Problems
ESA '93 Proceedings of the First Annual European Symposium on Algorithms
Algorithms for Reporting and Counting Geometric Intersections
IEEE Transactions on Computers
Generalized network Voronoi diagrams: Concepts, computational methods, and applications
International Journal of Geographical Information Science
Optimal construction of the city voronoi diagram
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
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We study the problem of moving network Voronoi diagram: given a network with n nodes and E edges. Suppose there are m sites (cars, postmen, etc) moving along the network edges, we design the algorithms to compute the dynamic network Voronoi diagram as sites move such that we can answer the nearest neighbor query efficiently. Furthermore, we extend it to the k-order dynamic network Voronoi diagram such that we can answer the k nearest neighbor query efficiently. We also study the problem when the query point is allowed to move at a given speed. Moreover, we give the algorithm for the half-online version of moving network Voronoi diagram.