## Abstract

A power assignment is an assignment of transmission power to each of the nodes of a wireless network, so that the induced communication graph has some desired properties. The cost of a power assignment is the sum of the powers. The energy of a transmission path from node u to node v is the sum of the squares of the distances between adjacent nodes along the path. For a constant t > 1, an energy t-spanner is a graph G′, such that for any two nodes u and v, there exists a path from u to v in G′, whose energy is at most t times the energy of a minimum-energy path from u to v in the complete Euclidean graph. In this paper, we study the problem of finding a power assignment, such that (1) its induced communication graph is a 'good' energy spanner, and (2) its cost is 'low'. We show that for any constant t > 1, one can find a power assignment, such that its induced communication graph is an energy t-spanner, and its cost is bounded by some constant times the cost of an optimal power assignment (where the sole requirement is strong connectivity of the induced communication graph). This is a significant improvement over the previous result due to Shpungin and Segal in Proceedings of 28th IEEE INFOCOM, pp 163-171, (2009).

Original language | English |
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Pages (from-to) | 1251-1258 |

Number of pages | 8 |

Journal | Wireless Networks |

Volume | 17 |

Issue number | 5 |

DOIs | |

State | Published - 1 Jul 2011 |

## Keywords

- Geometric spanners
- Power assignment

## ASJC Scopus subject areas

- Information Systems
- Computer Networks and Communications
- Electrical and Electronic Engineering