Improved Approximation Algorithms for Relay Placement

  • Alon Efrat
  • Sándor P. Fekete
  • Poornananda R. Gaddehosur
  • Joseph S. B. Mitchell
  • Valentin Polishchuk
  • Jukka Suomela
Conference paper

DOI: 10.1007/978-3-540-87744-8_30

Volume 5193 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Efrat A., Fekete S.P., Gaddehosur P.R., Mitchell J.S.B., Polishchuk V., Suomela J. (2008) Improved Approximation Algorithms for Relay Placement. In: Halperin D., Mehlhorn K. (eds) Algorithms - ESA 2008. ESA 2008. Lecture Notes in Computer Science, vol 5193. Springer, Berlin, Heidelberg

Abstract

In the relay placement problem the input is a set of sensors and a number r ≥ 1, the communication range of a relay. The objective is to place a minimum number of relays so that between every pair of sensors there is a path through sensors and/or relays such that the consecutive vertices of the path are within distance r if both vertices are relays and within distance 1 otherwise. We present a 3.11-approximation algorithm, and show that the problem admits no PTAS, assuming P\({}\ne{}\)NP.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Alon Efrat
    • 1
  • Sándor P. Fekete
    • 2
  • Poornananda R. Gaddehosur
    • 1
  • Joseph S. B. Mitchell
    • 3
  • Valentin Polishchuk
    • 4
  • Jukka Suomela
    • 4
  1. 1.Department of Computer ScienceUniversity of Arizona 
  2. 2.Department of Computer ScienceBraunschweig University of Technology 
  3. 3.Department of Applied Mathematics and StatisticsStony Brook University 
  4. 4.Helsinki Institute for Information Technology HIITUniversity of Helsinki and Helsinki University of Technology