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Computation of Non-dominated Points Using Compact Voronoi Diagrams

  • Binay Bhattacharya
  • Arijit Bishnu
  • Otfried Cheong
  • Sandip Das
  • Arindam Karmakar
  • Jack Snoeyink
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5942)

Abstract

We discuss in this paper a method of finding skyline or non-dominated points in a set P of n points with respect to a set S of m sites. A point p i  ∈ P is non-dominated if and only if for each p j  ∈ P, \(j \not= i\), there exists at least one point s ∈ S that is closer to p i than p j . We reduce this problem of determining non-dominated points to the problem of finding sites that have non-empty cells in an additively weighted Voronoi diagram under convex distance function. The weights of the said Voronoi diagram are derived from the co-ordinates of the points of P and the convex distance function is derived from S. In the 2-dimensional plane, this reduction gives a O((m + n)logm + n logn)-time randomized incremental algorithm to find the non-dominated points.

Keywords

Voronoi Diagram Query Point Voronoi Cell Additive Weight Lower Envelope 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Binay Bhattacharya
    • 1
  • Arijit Bishnu
    • 2
  • Otfried Cheong
    • 3
  • Sandip Das
    • 2
  • Arindam Karmakar
    • 2
  • Jack Snoeyink
    • 4
  1. 1.School of Computing ScienceSimon Fraser UniversityCanada
  2. 2.Advanced Computing and Microelectronics UnitIndian Statistical InstituteKolkataIndia
  3. 3.Department of Computer ScienceKorea Advanced Institute of Science and TechnologyDaejeonKorea
  4. 4.Department of Computer ScienceUniversity of North Carolina at Chapel HillUSA

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