Online Results for Black and White Bin Packing

János Balogh, József Békési, György Dósa, Leah Epstein, Hans Kellerer, Zsolt Tuza

Research output: Contribution to journalArticlepeer-review


In online bin packing problems, items of sizes in [0, 1] are to be partitioned into subsets of total size at most 1, called bins. We introduce a new variant where items are of two types, called black and white, and the item types must alternate in each bin, that is, two items of the same type cannot be assigned consecutively into a bin. This variant generalizes the standard online bin packing problem. We design an online algorithm with an absolute competitive ratio of 3. We further show that a number of well-known algorithms cannot have a better performance, even in the asymptotic sense. Interestingly, we show that this problem is harder than standard online bin packing by proving a general lower bound (Formula presented.) on the asymptotic competitive ratio of any deterministic or randomized online algorithm. This lower bound exceeds the upper bounds known for the absolute competitive ratio of standard online bin packing.

Original languageEnglish
Pages (from-to)137-155
Number of pages19
JournalTheory of Computing Systems
Issue number1
StatePublished - 1 Jan 2015

Bibliographical note

Publisher Copyright:
© 2014, Springer Science+Business Media New York.


  • Any Fit
  • Bin packing
  • Black and white bin packing
  • Competitive analysis
  • Conflict graphs
  • Online algorithms

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics


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