Elsevier

Journal of Algorithms

Volume 10, Issue 3, September 1989, Pages 305-326
Journal of Algorithms

On-line bin packing in linear time

https://doi.org/10.1016/0196-6774(89)90031-XGet rights and content

Abstract

In this paper, we study the 1-dimensional on-line bin packing problem. A list of pieces, each of size between zero and unity are to be packed, in order of their arrival, into a minimum number of unit-capacity bins. We present a new linear-time algorithm, the Modified Harmonic Algorithm and show, by a novel use of weighting functions, that it has an asymptotic worst-case performance ratio less than 32 + 19 + 1222 = 1.(615). We show that for a large class of linear-time on-line algorithms including the Modified Harmonic Algorithm, the performance ratio is at least 32 + 19 = 1.61. Then we show how to successively construct classes of improved linear-time on-line algorithms. For any algorithm in any of these classes, the performance ratio is at least 32 + 112 = 1.583. We present an improved algorithm called Modified Harmonic-2 with performance ratio 1.612 … and present an approach to construct linear-time on-line algorithms with better performance ratios. The analysis of Modified Harmonic-2 is omitted because it is very similar to that of Modified Harmonic, but it is substantially more complicated. Our results extend to orthogonal packings in two dimensions.

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Part of this author's work was performed when he was a graduate student at the University of Illinois, Urbana, IL. His work was supported in part by an IBM Graduate Fellowship.

This author's work was supported by the National Science Foundation under Grant NSF IST 80-12240 and the Joint Services Electronics Program (U.S. Army, U.S. Navy, and U.S. Air Force) under Contract N00014-79-C-0424.

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