Bounded space on-line bin packing: Best is better than first

J. Csirik, D. S. Johnson

Research output: Article

37 Citations (Scopus)


We present a sequence of new linear-time, bounded-space, on-line bin packing algorithms, the K-Bounded Best Fit algorithms (BBFK). They are based on the Θ (n log n) Best Fit algorithm in much the same way as the Next-K Fit algorithms are based on the Θ (n log n) First Fit algorithm. Unlike the Next-K Fit algorithms, whose asymptotic worst-case ratios approach the limiting value of 17/10 from above as K → ∞ but never reach it, these new algorithms have worst-case ratio 17/10 for all K > 2. They also have substantially better average performance than their bounded-space competition, as we have determined based on extensive experimental results summarized here for instances with item sizes drawn independently and uniformly from intervals of the form (0, u], 0 < u ≤ 1. Indeed, for each u < 1, it appears that there exists a fixed memory bound K(u) such that BBFK(u) obtains significantly better packings on average than does the First Fit algorithm, even though the latter requires unbounded storage and has a significantly greater running time. For u = 1, BBFK can still outperform First Fit (and essentially equal Best Fit) if K is allowed to grow slowly. We provide both theoretical and experimental results concerning the growth rates required.

Original languageEnglish
Pages (from-to)115-138
Number of pages24
JournalAlgorithmica (New York)
Issue number2
Publication statusPublished - jan. 1 2001

ASJC Scopus subject areas

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics

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