Advertisement

Reverse-Fit: A 2-optimal algorithm for packing rectangles

  • Ingo Schiermeyer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 855)

Abstract

We describe and analyze a ”level-oriented” algorithm, called ”Reverse-Fit”, for packing rectangles into a unit-width, infinite-height bin so as to minimize the total height of the packing. For L an arbitrary list of rectangles, all assumed to have width no more than 1, let h OPT denote the minimum possible bin height within the rectangles in L can be packed, and let RF(L) denote the height actually used by Reverse-Fit. We will show that RF(L)≤2·h OPT for an arbitrary list L of rectangles.

Key words

level-oriented packing algorithm bin-packing two-dimensional packing k-rectangle packing problem rectangle packing conjecture 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    B. S. Baker, E. G. Coffman, Jr. and R. L. Rivest, Orthogonal packings in two dimensions, SIAM J. Comput., Vol. 9, No. 4 (1980) 846–855.MathSciNetGoogle Scholar
  2. [2]
    P. Brucker and M. Grötschel, personal communication, January 1994.Google Scholar
  3. [3]
    E. G. Coffman, Jr., M. R. Garey, D. S. Johnson and R. E. Tarjan, Performance bounds for level-oriented two-dimensional packing algorithms, SIAM J. Comput., Vol. 9, No. 4 (1980) 808–826.MathSciNetGoogle Scholar
  4. [4]
    M. R. Garey and D. S. Johnson, Computers and Intractability, A Guide to the Theory of NP-Completeness, W. H. Freeman and Company, San Francisco, 1979.Google Scholar
  5. [5]
    D. D. K. D. B. Sleator, A 2.5 times optimal algorithm for packing in two dimensions, Inform. Process. Lett. 10, no. 1 (1980) 37–40.MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Ingo Schiermeyer
    • 1
  1. 1.Lehrstuhl C für MathematikTechnische Hochschule AachenAachenGermany

Personalised recommendations