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Further reflections on the one-dimensional packing problem

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Abstract

The one-dimensional packing problem may be stated as follows: When objects of lengthL are randomly placed on a line of lengthN until no more placement is possible, how much space remains unoccupied? In a previous paper, the authors showed that, forL = 2, the fraction of unoccupied space is dependent on the model governing the placement mechanism. In this paper, these results are extended from the discrete to the continuous case by allowing bothN andL to increase, while keeping their ratio constant. The methodology was validated by reproducing the analytical results for limiting cases.

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Authors and Affiliations

  1. Department of Information Systems, University of Maryland, 21228, Baltimore, MD, USA

    Richard W. Freedman

  2. Department of Chemistry, University of Maryland, 21228, Baltimore, MD, USA

    Fred Gornick

Authors
  1. Richard W. Freedman
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  2. Fred Gornick
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Freedman, R.W., Gornick, F. Further reflections on the one-dimensional packing problem. J Math Chem 13, 167–176 (1993). https://doi.org/10.1007/BF01165562

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  • DOI: https://doi.org/10.1007/BF01165562

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