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
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 discuss two variations of the moving network Voronoi diagram. The first one addresses the following problem: given a network with n vertices and E edges. Suppose there are m sites (cars, postmen, etc) moving along the network edges and we know their moving trajectories with time information. Which site is the nearest one to a point p located on network edge at time t′? We present an algorithm to answer this query in O(log(mW logm)) time with O(nmW log2m + n2logn + nE) time and O(nmW logm + E) space for preprocessing step, where E is the number of edges of the network graph (the definition of W is in section 3). The second variation views query point p as a customer with walking speed v. The question is which site he can catch the first? We can answer this query in O(m + log(mW logm)) time with same preprocessing time and space as the first case. If the customer is located at some node, then the query can be answered in O(log(mW logm)) time.