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The Complexity of Renaming Dan Alistarh

Summary: The Complexity of Renaming
Dan Alistarh
James Aspnes
Seth Gilbert
Rachid Guerraoui
We study the complexity of renaming, a fundamental problem in distributed computing in which a set of processes
need to pick distinct names from a given namespace. We prove an individual lower bound of (k) process steps for
deterministic renaming into any namespace of size sub-exponential in k, where k is the number of participants. This
bound is tight: it draws an exponential separation between deterministic and randomized solutions, and implies new
tight bounds for deterministic fetch-and-increment registers, queues and stacks. The proof of the bound is interesting
in its own right, for it relies on the first reduction from renaming to another fundamental problem in distributed
computing: mutual exclusion. We complement our individual bound with a global lower bound of (k log(k/c))
on the total step complexity of renaming into a namespace of size ck, for any c 1. This applies to randomized
algorithms against a strong adversary, and helps derive new global lower bounds for randomized approximate counter
and fetch-and-increment implementations, all tight within logarithmic factors.


Source: Aspnes, James - Department of Computer Science, Yale University


Collections: Computer Technologies and Information Sciences