### 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) |
---|---|

Article number | 20 |

Journal | ACM Transactions on Algorithms |

Volume | 12 |

Issue number | 2 |

DOIs | |

State | Published - Dec 1 2015 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics (miscellaneous)

### Cite this

*ACM Transactions on Algorithms*,

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

**Improved approximation algorithms for relay placement.** / Efrat, Alon; Fekete, Sándor P.; Mitchell, Joseph S B; Polishchuk, Valentin; Suomela, Jukka.

Research output: Contribution to journal › Article

*ACM Transactions on Algorithms*, vol. 12, no. 2, 20. https://doi.org/10.1145/2814938

}

TY - JOUR

T1 - Improved approximation algorithms for relay placement

AU - Efrat, Alon

AU - Fekete, Sándor P.

AU - Mitchell, Joseph S B

AU - Polishchuk, Valentin

AU - Suomela, Jukka

PY - 2015/12/1

Y1 - 2015/12/1

N2 - 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.

AB - 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.

KW - Approximation algorithms

KW - Polynomial-time approximation scheme (PTAS)

KW - Relays

KW - Sensor networks

KW - Steiner minimum spanning tree

KW - Wireless networks

UR - http://www.scopus.com/inward/record.url?scp=84954313620&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84954313620&partnerID=8YFLogxK

U2 - 10.1145/2814938

DO - 10.1145/2814938

M3 - Article

VL - 12

JO - ACM Transactions on Algorithms

JF - ACM Transactions on Algorithms

SN - 1549-6325

IS - 2

M1 - 20

ER -