## Abstract

A fundamental class of problems in wireless communication is concerned with the assignment of suitable transmission powers to wireless devices/stations such that the resulting communication graph satisfies certain desired properties and the overall energy consumed is minimized. Many concrete communication tasks in a wireless network like broadcast, multicast, point-to-point routing, creation of a communication backbone, etc. can be regarded as such a power assignment problem. This paper considers several problems of that kind; the first problem was studied before in [1,6] and aims to select and assign powers to k out of a total of n wireless network stations such that all stations are within reach of at least one of the selected stations. We show that the problem can be (1∈+∈ε) approximated by only looking at a small subset of the input, which is of size , i.e. independent of n and polynomial in k and 1/ε. Here d denotes the dimension of the space where the wireless devices are distributed, so typically d∈∈3 and describes the relation between the Euclidean distance between two stations and the power consumption for establishing a wireless connection between them. Using this coreset we are able to improve considerably on the running time of for the algorithm by Bilo et al. at ESA'05 ([6]) actually obtaining a running time that is linear in n. Furthermore we sketch how outliers can be handled in our coreset construction. The second problem deals with the energy-efficient, bounded-hop multicast operation: Given a subset C out of a set of n stations and a designated source node s we want to assign powers to the stations such that every node in C is reached by a transmission from s within k hops. Again we show that a coreset of size independent of n and polynomial in k, |C|, 1/ε exists, and use this to provide an algorithm which runs in time linear in n. The last problem deals with a variant of non-metric TSP problem where the edge costs are the squared Euclidean distances; this problem is motivated by data aggregation schemes in wireless sensor networks. We show that a good TSP tour under Euclidean edge costs can be very bad in the squared distance measure and provide a simple constant approximation algorithm, partly improving upon previous results in [5], [4].

Original language | English |
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Title of host publication | Distributed Computing in Sensor Systems - 4th IEEE International Conference, DCOSS 2008, Proceedings |

Pages | 282-295 |

Number of pages | 14 |

DOIs | |

State | Published - 1 Jul 2008 |

Event | 4th IEEE International Conference on Distributed Computing in Sensor Systems, DCOSS 2008 - Santorini Island, Greece Duration: 11 Jun 2008 → 14 Jun 2008 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 5067 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 4th IEEE International Conference on Distributed Computing in Sensor Systems, DCOSS 2008 |
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Country/Territory | Greece |

City | Santorini Island |

Period | 11/06/08 → 14/06/08 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science