About The Power of Anonymous Radio Networks
Résumé
We address the enumeration and the leader election problems over partially anonymous and multi-hop broadcast networks. We consider an asynchronous communication model where each process broadcasts a message and all its neighbours receive this message after arbitrary and unpredictable time. This amount of time depends on the processing time taken by the network layer to ensure message delivery. In this paper, we present necessary conditions that must satisfied by any graph to solve these problems and we show that these conditions are sufficient by providing an enumeration algorithm on the one hand and a leader election algorithm on the other hand. For both problems, we highlight the importance of the initial knowledge. Considering the enumeration problem, each node knows the size of the graph and, contrary to related works, the number of its neighbouring nodes is unknown. Whereas for the election problem, we show that this knowledge is not sufficient and we provide an election algorithm that assumes that each node initially knows a map of the network without knowing its position in this network. From the complexity viewpoint, our algorithms offer a better complexity in comparison with related works: the complexity (memory, messages and size of messages) decreases from exponential to polynomial.
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