 
Summary: Group Renaming
Yehuda Afek
Iftah Gamzu
Irit Levy§
Michael Merritt¶
Gadi Taubenfeld
Abstract
We study the group renaming problem, which is a natural generalization of the renaming
problem. An instance of this problem consists of n processors, partitioned into m groups, each
of at most g processors. Each processor knows the name of its group, which is in {1, . . . , M}.
The task of each processor is to choose a new name for its group such that processors from
different groups choose different new names from {1, . . . , }, where < M. We consider two
variants of the problem: a tight variant, in which processors of the same group must choose
the same new group name, and a loose variant, in which processors from the same group may
choose several different names. Our findings can be briefly summarized as follows:
1. We present an algorithm that solves the tight variant of the problem with = 2m1 in a
system consisting of gconsensus objects and atomic read/write registers. In addition, we
prove that it is impossible to solve this problem in a system having only (g1)consensus
objects and atomic read/write registers.
2. We devise an algorithm for the loose variant of the problem that only uses atomic
