Group Renaming

• Authors: Yehuda Afek;Iftah Gamzu;Irit Levy;Michael Merritt;Gadi Taubenfeld
• Venue: OPODIS '08 Proceedings of the 12th International Conference on Principles of Distributed Systems
• Year: 2008

We study the group renaming task, which is a natural generalization of the renaming task. An instance of this task 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 different names. Our findings can be briefly summarized as follows: 1 We present an algorithm that solves the tight variant of the problem with ***= 2m *** 1 in a system consisting of g -consensus objects and atomic read/write registers. In addition, we prove that it is impossible to solve this problem in a system having only (g *** 1)-consensus objects and atomic read/write registers. 1 We devise an algorithm for the loose variant of the problem that only uses atomic read/write registers, and has $\ell = 3n - \sqrt{n} - 1$. The algorithm also guarantees that the number of different new group names chosen by processors from the same group is at most $\min\{g, 2m, 2\sqrt{n}\}$. Furthermore, we consider the special case when the groups are uniform in size and show that our algorithm is self-adjusting to have ***= m (m + 1) / 2, when $m , and $\ell = 3n / 2 + m - \sqrt{n}/2 - 1$, otherwise.