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A Novel Approximation Algorithm for Minimum Geometric Disk Cover Problem with Hexagon Tessellation

  • Chi-Yu Chang
  • Chi-Chang Chen
  • Cheng-Chun Liu
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 20)

Abstract

Given a set P ofn points in the Euclidean plane, the minimum geometric disk cover (MGDC) problem is to identify a minimally sized set of congruent disks with prescribed radiusr that cover all the points in P. It is known that the MGDC problem is NP-complete. Solutions to the MGDC problem can be used to solve the relay node placement problems of wireless sensor networks. In this study, we proposed an approximation algorithm for the MGDC problem that identifies covering disks via the regular hexagon tessellation of the plane. We show that the approximation ratio of the proposed algorithm is 5. Furthermore, we show that if the set of points in P is uniformly distributed, then there is 41.7% probability for the proposed algorithm to use less than or equal to 5 times the optimal number of disks, and 58.3% probability of using no more than 4 times the optimal number of disks.

Keywords

Minimum Geometric Disk Cover Problem Hexagon Tessellation Relay Node Placement Problems Wireless Sensor Networks 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Information EngineeringI-Shou UniversityKaohsiung CityTaiwan

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