Improved Approximation Algorithms for Relay Placement

Authors:
Alon Efrat;Sándor P. Fekete;Poornananda R. Gaddehosur;Joseph S. Mitchell;Valentin Polishchuk;Jukka Suomela
Affiliations:
Department of Computer Science, University of Arizona,;Department of Computer Science, Braunschweig University of Technology,;Department of Computer Science, University of Arizona,;Department of Applied Mathematics and Statistics, Stony Brook University,;Helsinki Institute for Information Technology HIIT, University of Helsinki and Helsinki University of Technology,;Helsinki Institute for Information Technology HIIT, University of Helsinki and Helsinki University of Technology,
Venue:
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Year:
2008

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Abstract

In the relay placement problemthe input is a set of sensors and a number r茂戮驴 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 rif 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.