### Abstract

Wireless ad hoc radio networks have gained a lot of attention in recent years. We consider geometric networks, where nodes are located in a euclidean plane. We assume that each node has a variable transmission range and can learn the distance to the closest neighbor. We also assume that nodes have a special collision detection (CD) capability so that a transmitting node can detect a collision within its transmission range. We study the basic communication problem of collecting data from all nodes called convergecast. We measure the latency of convergecast, that is the number of time steps needed to collect the data in any n-node network. We propose a very simple randomized distributed algorithm that has the expected running time O(log n). We also show that this bound is tight and any algorithm needs Ω(log n) time steps while performing convergecast in an arbitrary network. One of the most important problems in wireless ad hoc networks is to minimize the energy consumption, which maximizes the network lifetime. We study the trade-off between the energy and the latency of convergecast. We show that our algorithm consumes at most O(n log n) times the minimum energy. We also demonstrate that for a line topology the minimum energy convergecast takes n - 1 time steps while any algorithm performing convergecast within O(log n) time steps requires Ω(n) times the minimum energy.

Original language | English (US) |
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Pages | 119-124 |

Number of pages | 6 |

DOIs | |

State | Published - Dec 1 2004 |

Externally published | Yes |

Event | 2nd Annual International Conference on Wireless On-Demand Network Systems and Services, WONS 2005 - St. Moritz, Switzerland Duration: Jan 19 2005 → Jan 21 2005 |

### Conference

Conference | 2nd Annual International Conference on Wireless On-Demand Network Systems and Services, WONS 2005 |
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Country | Switzerland |

City | St. Moritz |

Period | 1/19/05 → 1/21/05 |

### ASJC Scopus subject areas

- Computer Networks and Communications

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## Cite this

*Fast distributed algorithm for convergecast in Ad Hoc geometric radio networks*. 119-124. Paper presented at 2nd Annual International Conference on Wireless On-Demand Network Systems and Services, WONS 2005, St. Moritz, Switzerland. https://doi.org/10.1109/WONS.2005.17