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.
@article{arxiv.1102.4946,
title = {An Equivariance Theorem with Applications to Renaming (Preliminary Version)},
author = {Armando Castañeda and Maurice Herlihy and Sergio Rajsbaum},
journal= {arXiv preprint arXiv:1102.4946},
year = {2011}
}