### Abstract

In the network localization problem the locations of some nodes (called anchors) as well as the distances between some pairs of nodes are known, and the goal is to determine the location of all nodes. The localization problem is said to be solvable (or uniquely localizable) if there is a unique set of locations consistent with the given data. Recent results from graph rigidity theory made it possible to characterize the solvability of the localization problem in two dimensions. In this paper we address the following related optimization problem: given the set of known distances in the network, make the localization problem solvable by designating a smallest set of anchor nodes. We develop a polynomial-time 3-approximation algorithm for this problem by proving new structural results in graph rigidity and by using tools from matroid theory.

Original language | English |
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Title of host publication | Algorithmic Aspects of Wireless Sensor Networks - Second International Workshop ALGOSENSORS 2006, Revised Selected Papers |

Pages | 176-183 |

Number of pages | 8 |

DOIs | |

Publication status | Published - Dec 1 2006 |

Event | 2nd International Workshop on Algorithmic Aspects of Wireless Sensor Networks, ALGOSENSORS 2006 - Venice, Italy Duration: Jul 15 2006 → Jul 15 2006 |

### 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 | 4240 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 2nd International Workshop on Algorithmic Aspects of Wireless Sensor Networks, ALGOSENSORS 2006 |
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Country | Italy |

City | Venice |

Period | 7/15/06 → 7/15/06 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Algorithmic Aspects of Wireless Sensor Networks - Second International Workshop ALGOSENSORS 2006, Revised Selected Papers*(pp. 176-183). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4240 LNCS). https://doi.org/10.1007/11963271_16