Algebraic optimization: the Fermat-Weber location problem
Mathematical Programming: Series A and B
Distributed Anonymous Mobile Robots: Formation of Geometric Patterns
SIAM Journal on Computing
Leader Election Problem on Networks in which Processor Identity Numbers Are Not Distinct
IEEE Transactions on Parallel and Distributed Systems
Fault-tolerant gathering algorithms for autonomous mobile robots
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Remembering without memory: Tree exploration by asynchronous oblivious robots
Theoretical Computer Science
On the computational power of oblivious robots: forming a series of geometric patterns
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Byzantine agreement with homonyms
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Efficient algorithms for detecting regular point configurations
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
Biangular circle formation by asynchronous mobile robots
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
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In this paper, we consider the problem of formation of a series of geometric patterns 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 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 recent result of Das et al. 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.