Colorful bin packing

György Dósa, Leah Epstein

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Citations (Scopus)

Abstract

We study a variant of online bin packing, called colorful bin packing. In this problem, items that are presented one by one are to be packed into bins of size 1. Each item i has a size si ∈ [0,1] and a color c i ∈ C, where C is a set of colors (that is not necessarily known in advance). The total size of items packed into a bin cannot exceed its size, thus an item i can always be packed into a new bin, but an item cannot be packed into a non-empty bin if the previous item packed into that bin has the same color, or if the occupied space in it is larger than 1 - si. This problem generalizes standard online bin packing and online black and white bin packing (where |C| = 2). We prove that colorful bin packing is harder than black and white bin packing in the sense that an online algorithm for zero size items that packs the input into the smallest possible number of bins cannot exist for |C| ≥ 3, while it is known that such an algorithm exists for |C| = 2. We show that natural generalizations of classic algorithms for bin packing fail to work for the case |C| ≥ 3, and moreover, algorithms that perform well for black and white bin packing do not perform well either, already for the case |C| = 3. Our main results are a new algorithm for colorful bin packing that we design and analyze, whose absolute competitive ratio is 4, and a new lower bound of 2 on the asymptotic competitive ratio of any algorithm, that is valid even for black and white bin packing.

Original languageEnglish
Title of host publicationAlgorithm Theory, SWAT 2014 - 14th Scandinavian Symposium and Workshops, Proceedings
PublisherSpringer Verlag
Pages170-181
Number of pages12
ISBN (Print)9783319084039
DOIs
Publication statusPublished - Jan 1 2014
Event14th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2014 - Copenhagen, Denmark
Duration: Jul 2 2014Jul 4 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8503 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other14th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2014
CountryDenmark
CityCopenhagen
Period7/2/147/4/14

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Dósa, G., & Epstein, L. (2014). Colorful bin packing. In Algorithm Theory, SWAT 2014 - 14th Scandinavian Symposium and Workshops, Proceedings (pp. 170-181). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8503 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-08404-6_15