Recoverable, Abortable, and Adaptive Mutual Exclusion with Sublogarithmic RMR Complexity

TL;DR

This paper introduces a novel recoverable mutual exclusion algorithm that is abortable, adaptive to contention, and achieves sublogarithmic RMR complexity, improving efficiency in concurrent process synchronization.

Contribution

It presents the first RME algorithm with combined abortability, adaptiveness, and sublogarithmic RMR complexity, using new primitives and transformations.

Findings

Achieves $O(rac{ ext{log} N}{ ext{log} ext{log} N})$ worst-case RMR complexity.

Introduces a $D$-process abortable RME with $O(1)$ passage complexity.

Provides a transformation from low B complexity RME algorithms to adaptive lock algorithms.

Abstract

We present the first recoverable mutual exclusion (RME) algorithm that is simultaneously abortable, adaptive to point contention, and with sublogarithmic RMR complexity. Our algorithm has $O(\min(K,\log_W N))$ RMR passage complexity and $O(F + \min(K,\log_W N))$ RMR super-passage complexity, where $K$ is the number of concurrent processes (point contention), $W$ is the size (in bits) of registers, and $F$ is the number of crashes in a super-passage. Under the standard assumption that $W=\Theta(\log N)$, these bounds translate to worst-case $O(\frac{\log N}{\log \log N})$ passage complexity and $O(F + \frac{\log N}{\log \log N})$ super-passage complexity. Our key building blocks are: * A $D$-process abortable RME algorithm, for $D \leq W$, with $O(1)$ passage complexity and $O(1+F)$ super-passage complexity. We obtain this algorithm by using the Fetch-And-Add (FAA) primitive, unlike prior work on RME that uses Fetch-And-Store (FAS/SWAP). * A generic transformation that transforms any abortable RME algorithm with passage complexity of $B < W$, into an abortable RME lock with passage complexity of $O(\min(K,B))$.