An Equivariance Theorem with Applications to Renaming
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.
KeywordsChain Complex Prime Power Algebraic Topology Output Complex Protocol Complex
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