MaxMinSum Steiner Systems for Access-Balancing in Distributed Storage

TL;DR

This paper introduces MaxMinSum Steiner systems to improve server access balancing in distributed storage, optimizing the minimum sum of elements within blocks to enhance system performance.

Contribution

It proposes a new class of Steiner systems tailored for access balancing, and provides optimal and near-optimal labelings based on classical Steiner system constructions.

Findings

Proper relabelings achieve optimal MaxMin sums in Steiner triple systems.

Dual designs can be labeled within 3/4 of the optimal MaxMin sum.

The approach enhances server load balancing in distributed storage systems.

Abstract

Many code families such as low-density parity-check codes, fractional repetition codes, batch codes and private information retrieval codes with low storage overhead rely on the use of combinatorial block designs or derivatives thereof. In the context of distributed storage applications, one is often faced with system design issues that impose additional constraints on the coding schemes, and therefore on the underlying block designs. Here, we address one such problem, pertaining to server access frequency balancing, by introducing a new form of Steiner systems, termed MaxMinSum Steiner systems. MaxMinSum Steiner systems are characterized by the property that the minimum value of the sum of points (elements) within a block is maximized, or that the minimum sum of block indices containing some fixed point is maximized. We show that proper relabelings of points in the Bose and Skolem constructions for Steiner triple systems lead to optimal MaxMin values for the sums of interest; for the duals of the designs, we exhibit block labelings that are within a 3/4 multiplicative factor from the optimum.