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Point Location in the Continuous-Time Moving Network

  • Chenglin Fan
  • Jun Luo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6124)

Abstract

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(mWlogm)) time with O(nmWlog2 m + n 2logn + nE) time and O(nmWlogm + 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(mWlogm)) 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(mWlogm)) time.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Chenglin Fan
    • 1
    • 2
  • Jun Luo
    • 1
  1. 1.Shenzhen Institutes of Advanced TechnologyChinese Academy of SciencesChina
  2. 2.School of Information Science and EngineeringCentral South UniversityChangshaChina

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