Improved results for a memory allocation problem

TL;DR

This paper introduces a simpler online 3/2-approximation algorithm for a specialized bin packing problem with split items and at most two parts per bin, extending to a more general case with a 7/5-approximation.

Contribution

It presents a simpler online 3/2-approximation algorithm for the problem and analyzes its extension to the general case with a 7/5-approximation.

Findings

The problem is strongly NP-hard for the general case.

The proposed online algorithm achieves a 3/2-approximation.

An efficient 7/5-approximation algorithm is also provided.

Abstract

We consider a memory allocation problem that can be modeled as a version of bin packing where items may be split, but each bin may contain at most two (parts of) items. A 3/2-approximation algorithm and an NP-hardness proof for this problem was given by Chung et al. We give a simpler 3/2-approximation algorithm for it which is in fact an online algorithm. This algorithm also has good performance for the more general case where each bin may contain at most k parts of items. We show that this general case is also strongly NP-hard. Additionally, we give an efficient 7/5-approximation algorithm.