Approximation Algorithms for Demand Strip Packing

TL;DR

This paper introduces a new approximation algorithm for the Demand Strip Packing problem, improving the approximation ratio from 2 to 5/3+eps, and addresses special cases with optimal factors.

Contribution

It presents a (5/3+eps)-approximation algorithm for DSP, surpassing the previous 2-approximation, and provides optimal solutions for specific cases.

Findings

Achieved a (5/3+eps)-approximation for DSP.

Improved approximation ratios for special cases.

Established bounds matching known hardness results.

Abstract

In the Demand Strip Packing problem (DSP), we are given a time interval and a collection of tasks, each characterized by a processing time and a demand for a given resource (such as electricity, computational power, etc.). A feasible solution consists of a schedule of the tasks within the mentioned time interval. Our goal is to minimize the peak resource consumption, i.e. the maximum total demand of tasks executed at any point in time. It is known that DSP is NP-hard to approximate below a factor 3/2, and standard techniques for related problems imply a (polynomial-time) 2-approximation. Our main result is a (5/3+eps)-approximation algorithm for any constant eps>0. We also achieve best-possible approximation factors for some relevant special cases.