Integrated Bounds for Disintegrated Storage

TL;DR

This paper establishes fundamental space lower bounds for disintegrated storage systems, including Byzantine and coded storage, showing costs are exponential or linear depending on reader visibility, and these bounds match existing algorithms.

Contribution

It introduces integrated lower bounds for asynchronous wait-free emulations in disintegrated storage systems, unifying various models under a common framework.

Findings

Storage cost is exponential if readers are invisible.

Storage cost is linear if readers are visible.

Bounds are tight to known algorithms.

Abstract

We point out a somewhat surprising similarity between non-authenticated Byzantine storage, coded storage, and certain emulations of shared registers from smaller ones. A common characteristic in all of these is the inability of reads to safely return a value obtained in a single atomic access to shared storage. We collectively refer to such systems as disintegrated storage, and show integrated space lower bounds for asynchronous regular wait-free emulations in all of them. In a nutshell, if readers are invisible, then the storage cost of such systems is inherently exponential in the size of written values; otherwise, it is at least linear in the number of readers. Our bounds are asymptotically tight to known algorithms, and thus justify their high costs.