On Multiplicatively Weighted Voronoi Diagrams for Lines in the Plane

  • Kira Vyatkina
  • Gill Barequet
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6750)


We describe a method based on the wavefront propagation, which computes a multiplicatively weighted Voronoi diagram for a set L of n lines in the plane in O(n 2 logn) time and O(n 2) space. In the process, we derive complexity bounds and certain structural properties of such diagrams. An advantage of our approach over the general purpose machinery, which requires computation of the lower envelope of a set of halfplanes in three-dimensional space, lies in its relative simplicity. Besides, we point out that the unweighted Voronoi diagram for n lines in the plane has a simple structure, and can be obtained in optimal Θ(n 2) time and space.


Edge Event Voronoi Diagram Priority Queue Weighted Distance Active Point 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Kira Vyatkina
    • 1
  • Gill Barequet
    • 2
    • 3
  1. 1.Dept. of Mathematics and MechanicsSaint Petersburg State UniversitySt PetersburgRussia
  2. 2.Center for Graphics and Geometric Computing, Dept. of Computer ScienceThe Technion—Israel Institute of TechnologyHaifaIsrael
  3. 3.Dept. of Computer ScienceTufts UniversityMedfordUSA

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