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With the development of information technology, computing devices become more available and more connected, and are increasingly used in contexts where mobility plays an important role. Video games enable huge amounts of players to interact in some virtual world, and networks of connected vehicles are envisioned to improve road safety. In such distributed contexts, one cannot assume that each entity can share its position with all the participants. There is therefore a strong need for algorithms that maintain a number of valid properties related to the distances between the entities, while leading to a minimum number of message exchanges and computations. In this thesis, two problems are studied: enable two entities to efficiently estimate the distance between them, and enable them to answer to the following query: "which entities are situated at a distance less than a given value from me?".

Amphi LaBRI