Queries on Voronoi diagrams of moving points

O. Devillers, M. Golin, K. Kedem, S. Schirra

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


Suppose we are given n moving postmen described by their motion equations pi(t) = Si + vit, i = 1,...,n, where Si ∈ ℝ2 is the position of the ith postman at time t = 0, and vi ∈ ℝ2 is his velocity. The problem we address is how to preprocess the postmen data so as to be able to efficiently answer two types of nearest-neighbor queries. The first one asks "who is the nearest postman at time tq to a dog located at point sq. In the second type a query dog is located at point sq at time tq, its speed is vq > |vi| (for all i = 1,...,n), and we want to know which postman the dog can catch first. The first type of query is relatively simple to address, the second type at first seems much more complicated. We show that the problems are very closely related, with efficient solutions to the first type of query leading to efficient solutions to the second. We then present two solutions to these problems, with tradeoff between preprocessing time and query time. Both solutions use deterministic data structures.

Original languageEnglish
Pages (from-to)315-327
Number of pages13
JournalComputational Geometry: Theory and Applications
Issue number5
StatePublished - 1 Jan 1996


  • Dynamic computational geometry
  • Parametric search
  • Persistent data structures
  • Post-office problem
  • Voronoi diagram

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics


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