## Abstract

A wireless ad-hoc network is a collection of transceivers positioned in the plane. Each transceiver is equipped with a limited battery charge. The battery charge is then reduced after each transmission, depending on the transmission distance. One of the major problems in wireless network design is to route network traffic efficiently so as to maximize the network lifetime, i.e., the number of successful transmissions. In this paper we consider Rooted Maximum Lifetime Broadcast/Convergecast problems in wireless settings. The instance consists of a directed graph G = (V,E) with edge-weights {w(e) : e ∈ E}, node capacities {b(υ) : υ ∈ V}, and a root r. The goal is to find a maximum size collection {T _{1}, ..., T _{k} } of Broadcast/Convergecast trees rooted at r so that ∑_{i=1}^{k} w(δ_{Ti}(υ)) ≤ b (υ),, where δ _{T} (υ) is the set of edges leaving υ in T. In the Single Topology version all the Broadcast/Convergecast trees T _{i} are identical. We present a number of polynomial time algorithms giving constant ratio approximation for various broadcast and convergecast problems, improving previously known result of Ω(⌊1/log n ⌋)-approximation by [1]. We also consider a generalized Rooted Maximum Lifetime Mixedcast problem, where we are also given an integer γ≥ 0, and the goal is to find the maximum integer k so that k Broadcast and γk Convergecast rounds can be performed.

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 | 41-51 |

Number of pages | 11 |

DOIs | |

State | Published - 2009 |

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:We thank anonymous referees for their valuable comments that significantly improved the presentation of the paper. The second author was supported in part by US Air Force, European Office of Aerospace Research and Development, Grant# FA8655-09-1-3016.