An Algorithm for Online Two-dimensional Bin Packing with Two Open Bins

Abstract

Bin packing problem has been used for many applications. Its bounded space variant has more practical value because of the limited resources in the real world. In this paper, two-dimensional online bin packing problem with 2-bounded space is considered: A sequence of two-dimensional rectangles is asked to be packed into a minimum number of unit square bins. The packing is in an on-line manner that each rectangle item should be packed immediately upon its arrival. No two items overlap. Only two bins are available at any time. We extend the idea of one-bounded space rectangle packing by Zhang et al. [1] to 2-bounded space, modify the classification of items, pack items by using different strategies into two open bins and obtain a 4:4138-competitive ratio. Comparing to Zhang’s result of 5:155, this method is actually good when open two bins during the packing processing.