In an anonymous ring of n processors, all processors are totally indistinguishable except for their input values. These values are not necessarily distinct, i.e., they form a multiset, and this makes many problems particularly difficult. We consider the problem of distributively sorting such a multiset on the ring, and we give a complete characterization of the relationship with the problems of leader election for vertices and edges. For Boolean input values and prime n, we also establish a lower bound, and a reasonably close upper bound on the message complexity valid for sorting and leader election.

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Journal of Parallel and Distributed Computing
School of Computer Science

Flocchini, P. (Paola), Kranakis, E, Krizanc, D. (Danny), Luccio, F.L. (Flaminia L.), & Santoro, N. (2004). Sorting and election in anonymous asynchronous rings. Journal of Parallel and Distributed Computing, 64(2), 254–265. doi:10.1016/j.jpdc.2003.11.007