On the Construction of Generalized Voronoi Inverse of a Rectangular Tessellation

  • Sandip Banerjee
  • Bhargab B. Bhattacharya
  • Sandip Das
  • Arindam Karmakar
  • Anil Maheshwari
  • Sasanka Roy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8110)

Abstract

We introduce a new concept of constructing a generalized Voronoi inverse (GVI) of a given tessellation \({\mathcal T}\) of the plane. Our objective is to place a set S i of one or more sites in each convex region (cell) \(t_i \in{\mathcal T}\), such that all edges of \({\mathcal T}\) coincide with edges of Voronoi diagram V(S), where S = ∪  i S i , and ∀ i,j, i ≠ j, S i  ∩ S j  = ∅. Computation of GVI in general, is a difficult problem. In this paper, we study properties of GVI for the case when \(\mathcal T\) is a rectangular tessellation and propose an algorithm that finds a minimal set of sites S. We also show that for a general tessellation, a solution of GVI always exists.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Sandip Banerjee
    • 1
  • Bhargab B. Bhattacharya
    • 1
  • Sandip Das
    • 1
  • Arindam Karmakar
    • 2
  • Anil Maheshwari
    • 3
  • Sasanka Roy
    • 4
  1. 1.ACM UnitIndian Statistical InstituteKolkataIndia
  2. 2.Tezpur UniversityTezpurIndia
  3. 3.Carleton UniversityOttawaCanada
  4. 4.Chennai Mathematical InstituteChennaiIndia

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