Tel-aviv University Raymond and Beverly Sackler Faculty of Exact Sciences Blavatnik School of Computer Science

This thesis address 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. 2. We devise a {n, m, g}-independent algorithm for the loose variant of the problem that only uses atomic read/write registers, and has ` = 4n− 3. 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, 3√n−1}. Furthermore, we consider the special case when the groups are uniform in size and show that our algorithm is adaptive to have ` = 2m(m + 1) − 3, when m < √n, and ` = 4n− 3, otherwise.