## Abstract

In this paper we study the connectivity problem for wireless networks under the Signal to Interference plus Noise Ratio (SINR) model. Given a set of radio transmitters distributed in some area, we seek to build a directed strongly connected communication graph, and compute an edge coloring of this graph such that the transmitter-receiver pairs in each color class can communicate simultaneously. Depending on the interference model, more or less colors, corresponding to the number of frequencies or time slots, are necessary. We consider the SINR model that compares the received power of a signal at a receiver to the sum of the strength of other signals plus ambient noise . The strength of a signal is assumed to fade polynomially with the distance from the sender, depending on the so-called path-loss exponent α. We show that, when all transmitters use the same power, the number of colors needed is constant in one-dimensional grids if α> 1 as well as in two-dimensional grids if α> 2. For smaller path-loss exponents and two-dimensional grids we prove upper and lower bounds in the order of and Ω(logn/loglogn) for α= 2 and Θ(n ^{2/α- 1}) for α< 2 respectively. If nodes are distributed uniformly at random on the interval [0,1], a regular coloring of colors guarantees connectivity, while Ω(log logn) colors are required for any coloring.

Original language | English |
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Title of host publication | Algorithmic Aspects of Wireless Sensor Networks - 5th International Workshop, ALGOSENSORS 2009, Revised Selected Papers |

Pages | 116-127 |

Number of pages | 12 |

DOIs | |

State | Published - 2009 |

Externally published | Yes |

Event | 5th International Workshop on Algorithmic Aspects of Wireless Sensor Networks, ALGOSENSORS 2009 - Rhodes, Greece Duration: 10 Jul 2009 → 11 Jul 2009 |

### 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 | 5804 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 5th International Workshop on Algorithmic Aspects of Wireless Sensor Networks, ALGOSENSORS 2009 |
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Country/Territory | Greece |

City | Rhodes |

Period | 10/07/09 → 11/07/09 |

### Bibliographical note

Funding Information:Zvi Lotker and Francesco Pasquale were partially supported by a gift from Cisco Reseach Center.