Online algorithm for 1-space bounded multi-dimensional bin packing

  • Authors:

  • Yong Zhang;Francis Y. L. Chin;Hing-Fung Ting;Xin Han;Zhuo Chang

  • Affiliations:

  • College of Mathematics and Computer Science, Hebei University, China and Department of Computer Science, The University of Hong Kong, Hong Kong;Department of Computer Science, The University of Hong Kong, Hong Kong;Department of Computer Science, The University of Hong Kong, Hong Kong;School of Software, Dalian University of Technology, China;College of Mathematics and Computer Science, Hebei University, China

  • Venue:
  • FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
  • Year:
  • 2011

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Abstract

In this paper, we study 1-space bounded multi-dimensional bin packing. A sequence of items arrive over time, each item is a d-dimensional hyperbox and the length of each side is no more than 1. These items must be packed without overlapping into d-dimensional hypercubes with unit length on each side. In d-dimensional space, any two dimensions i and j define a space Pij. When an item arrives, we must pack it into an active bin immediately without any knowledge of the future items, and 90° -rotation on any plane Pij is allowed. The objective is to minimize the total number of bins used for packing all these items in the sequence. In the 1-space bounded variant, there is only one active bin for packing the current item. If the active bin does not have enough space to pack the item, it must be closed and a new active bin is opened. For this problem, we give an online algorithm with competitive ratio 4d, which is the first study on 1-space bounded d-dimensional bin packing.