Improved Approximation Algorithms for Relay Placement

In the relay placement problem the input is a set of sensors and a number r 1, the communication range of a relay. In the one-tier version of the problem 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. The two-tier version adds the restrictions that the path must go through relays, and not through sensors. We present a 3.11-approximation algorithm for the one-tier version and a PTAS for the two-tier version. We also show that the one-tier version admits no PTAS, assuming P = NP.

• Type: Conference
• Year: 2008
• Where: ESA
• Authors: Alon Efrat, Sándor P. Fekete, Poornananda R. Gaddehosur, Joseph S. B. Mitchell, Valentin Polishchuk, Jukka Suomela
• Keywords: Algorithms, ESA 2008, One-tier Version, Relay Placement Problem, Relays