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On the Construction of Generalized Voronoi Inverse of a Rectangular Tessellation

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Part of the Lecture Notes in Computer Science book series (TCOMPUTATSCIE,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.

Keywords

  • Heat Sink
  • Voronoi Diagram
  • Junction Point
  • Voronoi Region
  • Perpendicular Bisector

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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Banerjee, S., Bhattacharya, B.B., Das, S., Karmakar, A., Maheshwari, A., Roy, S. (2013). On the Construction of Generalized Voronoi Inverse of a Rectangular Tessellation. In: Gavrilova, M.L., Tan, C.J.K., Kalantari, B. (eds) Transactions on Computational Science XX. Lecture Notes in Computer Science, vol 8110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41905-8_3

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  • DOI: https://doi.org/10.1007/978-3-642-41905-8_3

  • Publisher Name: Springer, Berlin, Heidelberg

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