Sorting and election in anonymous asynchronous rings

Authors:
Paola Flocchini;Evangelos Kranakis;Danny Krizanc;Flaminia L. Luccio;Nicola Santoro
Affiliations:
School of Information Technology and Engineering, University of Ottawa, Ottawa, ON, Canada K1N 6N5;School of Computer Science, Carleton University, Ottawa, ON, Canada K1S 5B6;Mathematics Department, Wesleyan University, Middletown, CT;Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, Via Valerio 12/1, 34127 Trieste, Italy;School of Computer Science, Carleton University, Ottawa, ON, Canada K1S 5B6
Venue:
Journal of Parallel and Distributed Computing
Year:
2004

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Abstract

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.