Balanced and Swap-Robust Trades for Dynamical Distributed Storage

TL;DR

This paper introduces balanced and perturbation resilient trades for distributed storage, enhancing data privacy and access balancing by ensuring stable and flexible data arrangements across servers.

Contribution

It proposes a new class of balanced trades and perturbation resilient trades, with constructions based on number theory for improved data distribution and stability.

Findings

New balanced trade schemes for server access balancing

Perturbation resilient trades for data stability

Bounds established using number-theoretic methods

Abstract

Trades, introduced by Hedayat, are two sets of blocks of elements which may be exchanged (traded) without altering the counts of certain subcollections of elements within their constituent blocks. They are of importance in applications where certain combinations of elements dynamically become prohibited from being placed in the same group of elements, since in this case one can trade the offending blocks with allowed ones. This is particularly the case in distributed storage systems, where due to privacy and other constraints, data of some groups of users cannot be stored together on the same server. We introduce a new class of balanced trades, important for access balancing of servers, and perturbation resilient balanced trades, important for studying the stability of server access frequencies with respect to changes in data popularity. The constructions and bounds on our new trade schemes rely on specialized selections of defining sets in minimal trades and number-theoretic analyses.