An on-line algorithm for multidimensional bin packing

J. Csirik, André van Vliet

Research output: Contribution to journalArticle

50 Citations (Scopus)

Abstract

In this paper we present an on-line algorithm for the d-dimensional bin packing problem. We use the idea of rounding up the size of an item to a size that can be packed efficiently. Although our algorithm is not a generalization of the 1-dimensional HARMONICM algorithm [6], we can use its worst case analysis to prove that our algorithm yields an asymptotic worst case ratio of (1.691 ...)d. Further, we show that for uniformly distributed items the algorithm has an expected asymptotic efficiency of (2( 1 6π2 - 1))d.

Original languageEnglish
Pages (from-to)149-158
Number of pages10
JournalOperations Research Letters
Volume13
Issue number3
DOIs
Publication statusPublished - 1993

Fingerprint

Bin Packing
Bins
Worst-case Analysis
Bin Packing Problem
Asymptotic Efficiency
Rounding
Bin packing

Keywords

  • average case analysis
  • bin packing
  • on-line algorithms
  • worst-case analysis

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics
  • Modelling and Simulation

Cite this

An on-line algorithm for multidimensional bin packing. / Csirik, J.; van Vliet, André.

In: Operations Research Letters, Vol. 13, No. 3, 1993, p. 149-158.

Research output: Contribution to journalArticle

Csirik, J. ; van Vliet, André. / An on-line algorithm for multidimensional bin packing. In: Operations Research Letters. 1993 ; Vol. 13, No. 3. pp. 149-158.
@article{7a3e1a3b50634e32abd1e0e95be6a3a7,
title = "An on-line algorithm for multidimensional bin packing",
abstract = "In this paper we present an on-line algorithm for the d-dimensional bin packing problem. We use the idea of rounding up the size of an item to a size that can be packed efficiently. Although our algorithm is not a generalization of the 1-dimensional HARMONICM algorithm [6], we can use its worst case analysis to prove that our algorithm yields an asymptotic worst case ratio of (1.691 ...)d. Further, we show that for uniformly distributed items the algorithm has an expected asymptotic efficiency of (2( 1 6π2 - 1))d.",
keywords = "average case analysis, bin packing, on-line algorithms, worst-case analysis",
author = "J. Csirik and {van Vliet}, Andr{\'e}",
year = "1993",
doi = "10.1016/0167-6377(93)90004-Z",
language = "English",
volume = "13",
pages = "149--158",
journal = "Operations Research Letters",
issn = "0167-6377",
publisher = "Elsevier",
number = "3",

}

TY - JOUR

T1 - An on-line algorithm for multidimensional bin packing

AU - Csirik, J.

AU - van Vliet, André

PY - 1993

Y1 - 1993

N2 - In this paper we present an on-line algorithm for the d-dimensional bin packing problem. We use the idea of rounding up the size of an item to a size that can be packed efficiently. Although our algorithm is not a generalization of the 1-dimensional HARMONICM algorithm [6], we can use its worst case analysis to prove that our algorithm yields an asymptotic worst case ratio of (1.691 ...)d. Further, we show that for uniformly distributed items the algorithm has an expected asymptotic efficiency of (2( 1 6π2 - 1))d.

AB - In this paper we present an on-line algorithm for the d-dimensional bin packing problem. We use the idea of rounding up the size of an item to a size that can be packed efficiently. Although our algorithm is not a generalization of the 1-dimensional HARMONICM algorithm [6], we can use its worst case analysis to prove that our algorithm yields an asymptotic worst case ratio of (1.691 ...)d. Further, we show that for uniformly distributed items the algorithm has an expected asymptotic efficiency of (2( 1 6π2 - 1))d.

KW - average case analysis

KW - bin packing

KW - on-line algorithms

KW - worst-case analysis

UR - http://www.scopus.com/inward/record.url?scp=0027576155&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027576155&partnerID=8YFLogxK

U2 - 10.1016/0167-6377(93)90004-Z

DO - 10.1016/0167-6377(93)90004-Z

M3 - Article

VL - 13

SP - 149

EP - 158

JO - Operations Research Letters

JF - Operations Research Letters

SN - 0167-6377

IS - 3

ER -