### Abstract

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 polynomial-time approximation scheme (PTAS) for the two-tier version. We also show that the one-tier version admits no PTAS, assuming P ≠ NP.

Original language | English (US) |
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Article number | 20 |

Journal | ACM Transactions on Algorithms |

Volume | 12 |

Issue number | 2 |

DOIs | |

State | Published - Dec 1 2015 |

### Keywords

- Approximation algorithms
- Polynomial-time approximation scheme (PTAS)
- Relays
- Sensor networks
- Steiner minimum spanning tree
- Wireless networks

### ASJC Scopus subject areas

- Mathematics (miscellaneous)

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## Cite this

*ACM Transactions on Algorithms*,

*12*(2), [20]. https://doi.org/10.1145/2814938