## Abstract

Given a wireless network, we want to assign each node a transmission power, which will enable transmission between any two nodes (via other nodes). Moreover, due to possible faults, we want to have at least k vertex-disjoint paths from any node to any other, where k is some fixed integer, depending on the reliability of the nodes. The goal is to achieve this directed k-connectivity with a minimal overall power assignment. The problem is NP-Hard for any k ≥ 1 already for planar networks. Here we first present an optimal power assignment for uniformly spaced nodes on a line for any k ≥ 1. Based on it, we design an approximation algorithm for linear radio networks with factor min{2, (Δ/δ)^{α}}, where Δ and δ are the maximal and minimal distances between adjacent nodes respectively and parameter α ≥ 1 being the distance-power gradient. We then extend it to the weighted version. Finally, we develop an approximation algorithm with factor O(k^{2}), for planar case, which is, to the best of our knowledge, the first non-trivial result for this problem.

Original language | English |
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Title of host publication | Proceedings of the 2005 Joint Workshop on Foundations of Mobile Computing, Co-located with ACM/SIGMOBILE MobiCom 2005 |

Subtitle of host publication | DIALM-POMC 2005 |

Publisher | Association for Computing Machinery, Inc |

Pages | 89-96 |

Number of pages | 8 |

ISBN (Electronic) | 1595930922, 9781595930927 |

DOIs | |

State | Published - 2 Sep 2005 |

Event | 2005 Joint Workshop on Foundations of Mobile Computing, DIALM-POMC 2005 - Cologne, Germany Duration: 2 Sep 2005 → … |

### Conference

Conference | 2005 Joint Workshop on Foundations of Mobile Computing, DIALM-POMC 2005 |
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Country/Territory | Germany |

City | Cologne |

Period | 2/09/05 → … |

## Keywords

- Ad hoc networks
- Connectivity

## ASJC Scopus subject areas

- Computer Networks and Communications
- Software