 
Summary: The Complexity of Renaming
Dan Alistarh
EPFL
James Aspnes
Yale
Seth Gilbert
NUS
Rachid Guerraoui
EPFL
Abstract
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 subexponential 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 fetchandincrement 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 fetchandincrement implementations, all tight within logarithmic factors.
