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.
Bibliographical noteFunding Information:
A proceedings version where some of the results in this article were announced appeared as . Research supported in part by the Stiftung Aktion Österreich-Ungarn, project No. 82öu9, by the European Union and Hungary and co-financed by the European Social Fund through the project TÁMOP-4.2.2.C-11/1/KONV-2012-0004 - National Research Center for Development and Market Introduction of Advanced Information and Communication Technologies, the European Union and the European Social Fund through project ”Supercomputer, the national virtual lab” grant no.: TAMOP-4.2.2.C-11/1/KONV-2012-0010, the Chinese–Hungarian bilateral project TET-12-CN-1-2012-0028 and by the Hungarian Scientific Research Fund, grant OTKA 81493.
© 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