Anonymous Processors with Synchronous Shared Memory

TL;DR

This paper studies anonymous processors in synchronous shared memory systems, providing optimal algorithms for assigning unique identities under various conditions, including known or unknown number of processors and shared memory constraints.

Contribution

It introduces optimal Las Vegas and Monte Carlo algorithms for anonymous naming in shared memory systems, adapting to different knowledge and memory constraints.

Findings

Optimal expected time algorithms for known n

High probability correctness algorithms for unknown n

Use of O(n log n) random bits

Abstract

We consider synchronous distributed systems in which anonymous processors communicate by shared read-write variables. The goal is to have all the processors assign unique names to themselves. We consider the instances of this problem determined by whether the number $n$ is known or not, and whether concurrently attempting to write distinct values into the same memory cell is allowed or not, and whether the number of shared variables is a constant independent of $n$ or it is unbounded. For known $n$, we give Las Vegas algorithms that operate in the optimum expected time, as determined by the amount of available shared memory, and use the optimum $O(n\log n)$ expected number of random bits. For unknown $n$, we give Monte Carlo algorithms that produce correct output upon termination with probabilities that are $1-n^{-\Omega(1)}$, which is best possible when terminating almost surely and using $O(n\log n)$ random bits.