Tight results for Next Fit and Worst Fit with resource augmentation

Joan Boyar, Leah Epstein, Asaf Levin

Research output: Contribution to journalArticlepeer-review

Abstract

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
Volume411
Issue number26-28
DOIs
StatePublished - 6 Jun 2010

Bibliographical note

Funding Information:
The first author was partially supported by the Danish Natural Science Research Council (FNU).

Keywords

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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