# A Recoverable Mutex Algorithm with Sub-logarithmic RMR on Both CC and DSM

## TL;DR

This paper presents a recoverable mutex algorithm that achieves sub-logarithmic RMR complexity on both CC and DSM architectures, improving efficiency and resource usage over previous solutions.

## Contribution

It introduces a new recoverable mutex algorithm with sub-logarithmic RMR bounds applicable to both CC and DSM systems, with additional advantages like wait-freedom and minimal cache requirements.

## Key findings

- Achieves $O(rac{ ext{log} n}{ ext{log} ext{log} n})$ RMR bound on CC and DSM.
- Uses only Fetch-and-Store instruction for synchronization.
- Requires only $O(1)$ words cache per process on CC machines.

## Abstract

In light of recent advances in non-volatile main memory technology, Golab and Ramaraju reformulated the traditional mutex problem into the novel {\em Recoverable Mutual Exclusion} (RME) problem. In the best known solution for RME, due to Golab and Hendler from PODC 2017, a process incurs at most $O(\frac{\log n}{\log \log n})$ remote memory references (RMRs) per passage, where a passage is an interval from when a process enters the Try section to when it subsequently returns to Remainder. Their algorithm, however, guarantees this bound only for cache-coherent (CC) multiprocessors, leaving open the question of whether a similar bound is possible for distributed shared memory (DSM) multiprocessors. We answer this question affirmatively by designing an algorithm that satisfies the same complexity bound as Golab and Hendler's for both CC and DSM multiprocessors. Our algorithm has some additional advantages over Golab and Hendler's: (i) its Exit section is wait-free, (ii) it uses only the Fetch-and-Store instruction, and (iii) on a CC machine our algorithm needs each process to have a cache of only $O(1)$ words, while their algorithm needs $O(n)$ words.