### Abstract

In this paper, we introduce new geometric ad-hoc routing algorithms to route queries in static sensor networks. For single-source-queries routing, we utilise a centralised mechanism to accomplish a query using an asymptotically optimal number of transmissions O (c), where c is the length of the shortest path between the source and the destination. For multiple-source-queries routing, the number of transmissions for each query is bounded by O (c log n), where n is the number of nodes in the network. For both single-source and multiple-source queries, the routing stage is preceded by preprocessing stages requiring O (n D) and O (n^{2} D) transmissions, respectively, where D is the diameter of the network. Our algorithm improves the complexity of the currently best known algorithms in terms of the number of transmissions for each query. The preprocessing is worthwhile if it is followed by frequent queries. We could also imagine that there is an extra initial power (say, batteries) available during the preprocessing stage or alternatively the positions of the sensors are known in advance and the preprocessing can be done before the sensors are deployed in the field. It is also worth mentioning that a lower bound of Ω (c^{2}) transmissions has been proved if preprocessing is not allowed [F. Kuhn, R. Wattenhofer, A. Zollinger, Asymptotically optimal geometric mobile ad-hoc routing, in: Proceedings of the Sixth International Workshop on Discrete Algorithm and Methods for Mobility, Atlanta, GA, September 2002, pp. 24-33].

Original language | English (US) |
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Pages (from-to) | 1-11 |

Number of pages | 11 |

Journal | Journal of Discrete Algorithms |

Volume | 5 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 2007 |

Externally published | Yes |

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### Keywords

- Communication
- Design and analysis of algorithms
- Geometric routing
- Memory constraint
- Wireless sensor network

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

### Cite this

*Journal of Discrete Algorithms*,

*5*(1), 1-11. https://doi.org/10.1016/j.jda.2006.03.012