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 $p_i$ with a mapping function $\mathsf{{map}}_i()$ such that, for any two processes $p_i$ and $p_j$ and any integer $x\in [1..m]$, $\mathsf{{map}}_i(x)$ and $\mathsf{{map}}_j(x)$ allow them to address the same register.

Let n be the number of processes and $\alpha$ a positive integer. The article presents election and de-anonymization algorithms for $m=\alpha ~ n +\beta$ registers, where $\beta$ 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.