Anonymous read/write memory: Leader election and de-anonymization

Abstract

Anonymity has mostly been studied in the context where processes have no identity. A new notion of anonymity was recently introduced at PODC 2017, namely, this notion considers that the processes have distinct identities but disagree on the names of the read/write registers that define the shared memory. As an example, a register named A by a process p and a shared register named B by another process q may correspond to the very same register X, while the same name C may correspond to different registers for p and q. Recently, a memory-anonymous deadlock-free mutual exclusion algorithm has been proposed by some of the authors. This article addresses two different problems, namely election and memory de-anonymization. Election consists of electing a single process as a leader that is known by every process. Considering the shared memory as an array of atomic read/write registers SM [1.m], memory de-anonymization consists in providing each process pi with a mapping function mapi() such that, for any two processes pi and pj and any integer x ∈[l..m], mapi(x) and mapj(x) allow them to address the same register. Let n be the number of processes and α a positive integer. The article presents election and de-anonymization algorithms for m = α n+ β registers, where β is equal to 1, n−1, or belongs to a set denoted M(n) (which characterizes the values for which mutual exclusion can be solved despite anonymity). The de-anonymization algorithms are based on the use of election algorithms. The article also shows that the size of the permanent control information that, due to de-anonymization, a register must save forever, can be reduced to a single bit.