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Robot Networks with Homonyms: The Case of Patterns Formation

Abstract : In this paper, we consider the problem of formation of a series of geometric patterns [4] by a network of oblivious mobile robots that communicate only through vision. So far, the problem has been studied in models where robots are either assumed to have distinct identifiers or to be completely anonymous. To generalize these results and to better understand how anonymity affects the computational power of robots, we study the problem in a new model, introduced recently in [5], in which n robots may share up to 1 <= h <= n different identifiers. We present necessary and sufficient conditions, relating symmetricity and homonymy, that makes the problem solvable. We also show that in the case where h = n, making the identifiers of robots invisible does not limit their computational power. This contradicts a result of [4]. To present our algorithms, we use a function that computes the Weber point for many regular and symmetric configurations. This function is interesting in its own right, since the problem of finding Weber points has been solved up to now for only few other patterns.
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https://hal.inria.fr/inria-00596626
Contributor : Zohir Bouzid Connect in order to contact the contributor
Submitted on : Saturday, May 28, 2011 - 5:03:08 AM
Last modification on : Sunday, June 26, 2022 - 9:52:59 AM
Long-term archiving on: : Monday, August 29, 2011 - 2:25:31 AM

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  • HAL Id : inria-00596626, version 1
  • ARXIV : 1105.5817

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Zohir Bouzid, Anissa Lamani. Robot Networks with Homonyms: The Case of Patterns Formation. [Research Report] 2011. ⟨inria-00596626⟩

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