Dynamic bin packing of unit fractions items

Authors:
Wun-Tat Chan;Tak-Wah Lam;Prudence W. H. Wong
Affiliations:
Department of Computer Science, University of Hong Kong, Hong Kong;Department of Computer Science, University of Hong Kong, Hong Kong;Department of Computer Science, University of Liverpool, UK
Venue:
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Year:
2005

Citing 13
Cited 3

Bin packing with divisible item sizes

Journal of Complexity
Improved bounds for harmonic-based bin packing algorithms

Discrete Applied Mathematics - Special volume: combinatorics and theoretical computer science
An improved lower bound for on-line bin packing algorithms

Information Processing Letters
Approximation algorithms for bin packing: a survey

Approximation algorithms for NP-hard problems
Online computation and competitive analysis

Online computation and competitive analysis
Fully Dynamic Algorithms for Bin Packing: Being (Mostly) Myopic Helps

SIAM Journal on Computing
Bin Packing with Discrete Item Sizes, Part I: Perfect Packing Theorems and the Average Case Behavior of Optimal Packings

SIAM Journal on Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
On the online bin packing problem

Journal of the ACM (JACM)
On-line Packing and Covering Problems

Developments from a June 1996 seminar on Online algorithms: the state of the art
Windows Scheduling Problems for Broadcast Systems

SIAM Journal on Computing
Windows scheduling as a restricted version of Bin Packing

SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
On-line windows scheduling of temporary items

ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation

2005: an offline persepctive

ACM SIGACT News
Windows scheduling as a restricted version of bin packing

ACM Transactions on Algorithms (TALG)
On dynamic bin packing: an improved lower bound and resource augmentation analysis

COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper studies the dynamic bin packing problem, in which items arrive and depart at arbitrary time. We want to pack a sequence of unit fractions items (i.e., items with sizes 1/w for some integer w ≥ 1) into unit-size bins such that the maximum number of bins used over all time is minimized. Tight and almost-tight performance bounds are found for the family of any-fit algorithms, including first-fit, best-fit, and worst-fit. We show that the competitive ratio of best-fit and worst-fit is 3, which is tight, and the competitive ratio of first-fit lies between 2.45 and 2.4985. We also show that no on-line algorithm is better than 2.428-competitive. This result improves the lower bound of dynamic bin packing problem even for general items.