An equivariance theorem with applications to renaming

Authors:
Armando Castañeda;Maurice Herlihy;Sergio Rajsbaum
Affiliations:
IRISA-INRIA, Rennes Cedex, France;Computer Science Department, Brown University, Providence, RI;Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico
Venue:
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Year:
2012

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Abstract

In the renaming problem, each process in a distributed system is issued a unique name from a large name space, and the processes must coordinate with one another to choose unique names from a much smaller name space. We show that lower bounds on the solvability of renaming in an asynchronous distributed system can be formulated as a purely topological question about the existence of an equivariant chain map from a "topological disk" to a "topological annulus". Proving the non-existence of such a map implies the non-existence of a distributed renaming algorithm in several related models of computation.