On data reduction for dynamic vector bin packing

TL;DR

This paper investigates the complexity of data reduction in dynamic vector bin packing and introduces an efficient algorithm that significantly reduces instance sizes while maintaining near-optimal solutions.

Contribution

It demonstrates hardness results for instance shrinking and proposes a polynomial-time data reduction method for approximate solutions.

Findings

Hardness results for polynomial shrinking of DVBP instances.

A simple data reduction algorithm achieves (1+ε)-approximate solutions.

Instance sizes from real cloud data are reduced by an order of magnitude.

Abstract

We study a dynamic vector bin packing (DVBP) problem. We show hardness for shrinking arbitrary DVBP instances to size polynomial in the number of request types or in the maximal number of requests overlapping in time. We also present a simple polynomial-time data reduction algorithm that allows to recover $(1 + {\varepsilon})$-approximate solutions for arbitrary ${\varepsilon} > 0$. It shrinks instances from Microsoft Azure and Huawei Cloud by an order of magnitude for ${\varepsilon} = 0.02$.