New Bounds for Variable-Sized Online Bin Packing
Abstract
In the variable-sized online bin packing problem, one has to assign items to bins one by one. The bins are drawn from some fixed set of sizes, and the goal is to minimize the sum of the sizes of the bins used. We present new algorithms for this problem and show upper bounds for them which improve on the best previous upper bounds. We also show the first general lower bounds for this problem. The case in which bins of two sizes, 1 and $\alpha \in (0,1)$, are used is studied in detail. This investigation leads us to the discovery of several interesting fractal-like curves.
MSC codes
Keywords
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
D. J. Brown, A Lower Bound for On‐Line One‐Dimensional Bin Packing Algorithms, Tech. report R‐864, Coordinated Science Laboratory, Urbana, IL, 1979.
2.
Barun Chandra, Does randomization help in on‐line bin packing?, Inform. Process. Lett., 43 (1992), 15–19
3.
E. G. Coffman, M. R. Garey, and D. S. Johnson, Approximation algorithms for bin packing: A survey, in Approximation Algorithms for NP‐Hard Problems, D. Hochbaum, ed., PWS Publishing, Boston, 1997, Chap. 2.
4.
J. Csirik, An on‐line algorithm for variable‐sized bin packing, Acta Inform., 26 (1989), 697–709
5.
János Csirik, Gerhard Woeginger, On‐line packing and covering problems, Lecture Notes in Comput. Sci., Vol. 1442, Springer, Berlin, 1998, 147–177
6.
Leah Epstein, Online variable sized covering, Inform. and Comput., 171 (2001), 294–305
7.
D. Friesen, M. Langston, A storage‐size selection problem, Inform. Process. Lett., 18 (1984), 295–296
8.
D. K. Friesen and M. A. Langston, Variable sized bin packing, SIAM J. Comput., 15 (1986), pp. 222–230.
9.
D. S. Johnson, Near‐Optimal Bin Packing Algorithms, Ph.D. thesis, MIT, Cambridge, MA, 1973.
10.
D. S. Johnson, Fast algorithms for bin packing, J. Comput. System Sci., 8 (1974), pp. 272–314.
11.
D. S. Johnson, A. Demers, J. D. Ullman, M. R. Garey, and R. L. Graham, Worst‐case performance bounds for simple one‐dimensional packing algorithms, SIAM J. Comput., 3 (1974), pp. 299–325.
12.
Nancy Kinnersley, Michael Langston, Online variable‐sized bin packing, Discrete Appl. Math., 22 (1988/89), 143–148
13.
C. Lee, D. Lee, A simple on‐line bin‐packing algorithm, J. Assoc. Comput. Mach., 32 (1985), 562–572
14.
Frank Liang, A lower bound for on‐line bin packing, Inform. Process. Lett., 10 (1980), 76–79
15.
Prakash Ramanan, Donna Brown, C. Lee, D. Lee, On‐line bin packing in linear time, J. Algorithms, 10 (1989), 305–326
16.
Michael Richey, Improved bounds for harmonic‐based bin packing algorithms, Discrete Appl. Math., 34 (1991), 203–227, Combinatorics and theoretical computer science (Washington, DC, 1989)
17.
S. S. Seiden, On the online bin packing problem, in Proceedings of the 28th International Colloquium on Automata, Languages and Programming, Crete, Greece, 2001, pp. 237–249.
18.
Steven Seiden, An optimal online algorithm for bounded space variable‐sized bin packing, SIAM J. Discrete Math., 14 (2001), 458–470
19.
André van Vliet, An improved lower bound for on‐line bin packing algorithms, Inform. Process. Lett., 43 (1992), 277–284
20.
Gerhard Woeginger, Guochuan Zhang, Optimal on‐line algorithms for variable‐sized bin covering, Oper. Res. Lett., 25 (1999), 47–50
21.
Andrew Yao, New algorithms for bin packing, J. Assoc. Comput. Mach., 27 (1980), 207–227
Information & Authors
Information
Published In
SIAM Journal on Computing
Pages: 455 - 469
ISSN (online): 1095-7111
Copyright
Copyright © 2003 Society for Industrial and Applied Mathematics.
History
Published online: 17 February 2012
MSC codes
Keywords
Authors
Metrics & Citations
Metrics
Citations
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited By
- Cost-Effective App User Allocation in an Edge Computing EnvironmentIEEE Transactions on Cloud Computing, Vol. 10, No. 3 | 1 Jul 2022
- Fulfillment scheduling for buy‐online‐pickup‐in‐store ordersProduction and Operations Management, Vol. 31, No. 7 | 1 July 2022
- On-line three-dimensional packing problems: A review of off-line and on-line solution approachesComputers & Industrial Engineering, Vol. 168 | 1 Jun 2022
- Irreducible bin packing and normality in routing open shopAnnals of Mathematics and Artificial Intelligence, Vol. 89, No. 8-9 | 22 June 2021
- A new model for Last-Mile Delivery and Satellite Depots management: The impact of the on-demand economyTransportation Research Part E: Logistics and Transportation Review, Vol. 145 | 1 Jan 2021
- Irreducible Bin Packing: Complexity, Solvability and Application to the Routing Open ShopLearning and Intelligent Optimization | 22 January 2020
- Lower bounds for a bin packing problem with linear usage costEuropean Journal of Operational Research, Vol. 274, No. 1 | 1 Apr 2019
- Variable Neighborhood Search Algorithm for the Variable Cost and Size Bin Packing ProblemHandbook of Research on Metaheuristics for Order Picking Optimization in Warehouses to Smart Cities | 1 Jan 2019
- Bin Packing Problems (Promising Models and Examples)Journal of Communications Technology and Electronics, Vol. 63, No. 6 | 4 July 2018
- Generating Bin Packing Heuristic Through Grammatical Evolution Based on Bee Swarm OptimizationNature-Inspired Design of Hybrid Intelligent Systems | 10 December 2016
- Improving operating room schedulesHealth Care Management Science, Vol. 19, No. 3 | 17 February 2015
- Online bin packing with (1,1) and (2, $$R$$ R ) binsJournal of Combinatorial Optimization, Vol. 30, No. 2 | 16 May 2014
- Virtual machine placement with two-path traffic routing for reduced congestion in data center networksComputer Communications, Vol. 53 | 1 Nov 2014
- Improving the Bin Packing Heuristic through Grammatical Evolution Based on Swarm IntelligenceMathematical Problems in Engineering, Vol. 2014 | 1 Jan 2014
- Evolving and reusing Bin Packing heuristic through Grammatical Differential Evolution2013 World Congress on Nature and Biologically Inspired Computing | 1 Aug 2013
- Online Bin Packing with (1,1) and (2,R) BinsCombinatorial Optimization and Applications | 1 Jan 2013
- The Train Delivery Problem RevisitedAlgorithms and Computation | 1 Jan 2013
- Bin Packing Approximation Algorithms: Survey and ClassificationHandbook of Combinatorial Optimization | 26 July 2013
- The generalized bin packing problemTransportation Research Part E: Logistics and Transportation Review, Vol. 48, No. 6 | 1 Nov 2012
- Vector bin packing with multiple-choiceDiscrete Applied Mathematics, Vol. 160, No. 10-11 | 1 Jul 2012
- New lower bounds for certain classes of bin packing algorithmsTheoretical Computer Science, Vol. 440-441 | 1 Jul 2012
- Stochastic VM Multiplexing for Datacenter Consolidation2012 IEEE Ninth International Conference on Services Computing | 1 Jun 2012
- Grammatical Evolution of Local Search HeuristicsIEEE Transactions on Evolutionary Computation, Vol. 16, No. 3 | 1 Jun 2012
- Automating the Packing Heuristic Design Process with Genetic ProgrammingEvolutionary Computation, Vol. 20, No. 1 | 1 Mar 2012
- Efficient lower bounds and heuristics for the variable cost and size bin packing problemComputers & Operations Research, Vol. 38, No. 11 | 1 Nov 2011
- Comparing VM-Placement Algorithms for On-Demand Clouds2011 IEEE Third International Conference on Cloud Computing Technology and Science | 1 Nov 2011
- New Lower Bounds for Certain Classes of Bin Packing AlgorithmsApproximation and Online Algorithms | 1 Jan 2011
- Cloud Storage and Online Bin PackingIntelligent Distributed Computing V | 1 Jan 2011
- Vector Bin Packing with Multiple-ChoiceAlgorithm Theory - SWAT 2010 | 1 Jan 2010
- Variable Sized Online Interval Coloring with BandwidthAlgorithmica, Vol. 53, No. 3 | 13 October 2007
- Bin packing with controllable item sizesInformation and Computation, Vol. 206, No. 8 | 1 Aug 2008
- An On-Line Access Selection Algorithm for ABC Networks Supporting Elastic Services2008 IEEE Wireless Communications and Networking Conference | 1 Mar 2008
- An APTAS for Generalized Cost Variable-Sized Bin PackingSIAM Journal on Computing, Vol. 38, No. 1 | 23 April 2008
- Transmission Link Dimensioning and Service Assignment for Differentiated ProtectionJournal of Network and Systems Management, Vol. 14, No. 4 | 17 October 2006
- Online Bin Packing with Cardinality ConstraintsSIAM Journal on Discrete Mathematics, Vol. 20, No. 4 | 15 December 2006
- Variable Sized Online Interval Coloring with BandwidthAlgorithm Theory – SWAT 2006 | 1 Jan 2006
- Online Bin Packing with Cardinality ConstraintsAlgorithms – ESA 2005 | 1 Jan 2005
- Simulative Analysis of Access Selection Algorithms for Multi-Access Networks2006 International Symposium on a World of Wireless, Mobile and Multimedia Networks(WoWMoM'06)
View Options
Get Access
- Access via your Institution
- Questions about how to access this content? Contact SIAM at [email protected].