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A Facility Coloring Problem in 1-D

  • Sandip Das
  • Anil Maheshwari
  • Ayan Nandy
  • Michiel Smid
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8546)

Abstract

Consider a line segment R consisting of n facilities. Each facility is a point on R and it needs to be assigned exactly one of the colors from a given palette of c colors. At an instant of time only the facilities of one particular color are ‘active’ and all other facilities are ‘dormant’. For the set of facilities of a particular color, we compute the one dimensional Voronoi diagram, and find the cell, i.e, a segment of maximum length. The users are assumed to be uniformly distributed over R and they travel to the nearest among the facilities of that particular color that is active. Our objective is to assign colors to the facilities in such a way that the length of the longest cell is minimized. We solve this optimization problem for various values of n and c. We propose an optimal coloring scheme for the number of facilities n being a multiple of c as well as for the general case where n is not a multiple of c. When n is a multiple of c, we compute an optimal scheme in Θ(n) time. For the general case, we propose a coloring scheme that returns the optimal in O(n 2logn) time.

Keywords

Objective Function Wireless Sensor Network Voronoi Diagram Voronoi Cell Distance Vector 
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 International Publishing Switzerland 2014

Authors and Affiliations

  • Sandip Das
    • 1
  • Anil Maheshwari
    • 2
  • Ayan Nandy
    • 1
  • Michiel Smid
    • 2
  1. 1.Indian Statistical InstituteKolkataIndia
  2. 2.School of Computer ScienceCarleton UniversityOttawaCanada

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