Tight Lower Bounds for the RMR Complexity of Recoverable Mutual Exclusion

TL;DR

This paper establishes a tight lower bound on the remote memory reference complexity for recoverable mutual exclusion algorithms, showing that they inherently require at least logarithmic RMRs, matching the best known upper bounds.

Contribution

It proves a fundamental lower bound on RMR complexity for RME algorithms using common primitives, unifying and extending prior bounds and assumptions.

Findings

RMR complexity lower bound of (aaf4af4 n/af7af7 af4af4 af7af7 n) for RME algorithms.

Lower bound applies to algorithms using atomic read, write, fetch-and-store, fetch-and-increment, compare-and-swap.

Matches the best upper bounds, indicating optimality of existing algorithms.

Abstract

We present a tight RMR complexity lower bound for the recoverable mutual exclusion (RME) problem, defined by Golab and Ramaraju \cite{GR2019a}. In particular, we show that any $n$-process RME algorithm using only atomic read, write, fetch-and-store, fetch-and-increment, and compare-and-swap operations, has an RMR complexity of $\Omega(\log n/\log\log n)$ on the CC and DSM model. This lower bound covers all realistic synchronization primitives that have been used in RME algorithms and matches the best upper bounds of algorithms employing swap objects (e.g., [5,6,10]). Algorithms with better RMR complexity than that have only been obtained by either (i) assuming that all failures are system-wide [7], (ii) employing fetch-and-add objects of size $(\log n)^{\omega(1)}$ [12], or (iii) using artificially defined synchronization primitives that are not available in actual systems [6,9].