Closed on-line bin packing

  • Authors:

  • E. Asgeirsson;U. Ayesta;E. Coffman;J. Etra;P. Momcilovic;D. Phillips;V. Vokhshoori;Z. Wang;J. Wolfe

  • Affiliations:

  • Department of Industrial Engineering and Operations Research, Columbia University, New York, NY;INRIA, 2004 Route des Lucioles, Sophia Antipolis Cedex, France;Department of Electrical Engineering, Columbia University, New York, NY;Columbia Law School, Columbia University, New York, NY;Department of Electrical Engineering, Columbia University, New York, NY;Department of Industrial Engineering and Operations Research, Columbia University, New York, NY;Department of Electrical Engineering, Columbia University, New York, NY;Graduate School of Business, Columbia University, New York, NY;Department of Electrical Engineering, Columbia University, New York, NY

  • Venue:
  • Acta Cybernetica
  • Year:
  • 2002

Quantified Score

Hi-index 0.00

Visualization

Abstract

An optimal algorithm for the classical bin packing problem partitions (packs) a given set of items with sizes at most 1 into a smallest number of unit-capacity bins such that the sum of the sizes of the items in each bin is at most 1. Approximation algorithms for this NP-hard problem are called on-line if the items are packed sequentially into bins with the bin receiving a given item being independent of the number and sizes of all items as yet unpacked. Off-line algorithms plan packings assuming full (advance) knowledge of all item sizes. The closed on-line algorithms are intermediate: item sizes are not known in advance but the number n of items is. The uniform model, where the n item sizes are independent uniform random draws from [0,1], commands special attention in the average-case analysis of bin packing algorithms. In this model, the expected wasted space produced by an optimal off-line algorithm is Θ(√n), while that produced by an optimal on-line algorithm is Θ(√n log n). Surprisingly, an optimal closed on-line algorithm also wastes only Θ(√n) space on the average. A proof of this last result is the principal contribution of this paper. However, we also identify a class of optimal closed algorithms, extend the main result to other probability models, and give an estimate of the hidden constant factor.