Tight results for Next Fit and Worst Fit with resource augmentation

Joan Boyar, Leah Epstein, Asaf Levin

Research output: Contribution to journalArticlepeer-review


It is well known that the two simple algorithms for the classic bin packing problem, NF and WF both have an approximation ratio of 2. However, WF seems to be a more reasonable algorithm, since it never opens a new bin if an existing bin can still be used. Using resource augmented analysis, where the output of an approximation algorithm, which can use bins of size b > 1, is compared to an optimal packing into bins of size 1, we give a complete analysis of the asymptotic approximation ratio of WF and of NF, and use it to show that WF is strictly better than NF for any 1 < b < 2, while they have the same asymptotic performance guarantee for all b ≥ 2, and for b = 1.

Original languageEnglish
Pages (from-to)2572-2580
Number of pages9
JournalTheoretical Computer Science
Issue number26-28
StatePublished - 6 Jun 2010

Bibliographical note

Funding Information:
The authors gratefully acknowledge support from the National Natural Science Foundation of China (91434202, 21506127), the Program for Changjiang Scholars and Innovative Research Team in University (IRT15R48), State Key Laboratory of Polymer Materials Engineering (sklpme2014-1-01), and State Key Laboratory of Separation Membranes and Membrane Processes (Tianjin Polytechnic University, No. M2-201506).


  • Bin packing
  • Next Fit
  • Resource augmentation
  • Worst Fit

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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