Fair versus Unrestricted Bin Packing
We consider the Unrestricted Bin Packing problem where we have bins of equal size and a sequence of items. The goal is to maximize the number of items that are packed in the bins by an on-line algorithm. We investigate the power of performing admission control on the items, i.e., rejecting items while there is enough space to pack them, versus behaving fairly, i.e., rejecting an item only when there is not enough space to pack it. We show that by performing admission control on the items, we get better performance for various measures compared with the performance achieved on the fair version of the problem. Our main result shows that we can pack 2/3 of the items for sequences in which the optimal can pack all the items.
KeywordsCompetitive Ratio Online Algorithm Large Item Small Item Request Sequence
Unable to display preview. Download preview PDF.
- 1.B. Awerbuch, Y. Azar, and S. Plotkin. Throughput-Competitive On-Line Routing. In 34th IEEE Symposium on Foundations of Computer Science, pages 32–40, 1993.Google Scholar
- 2.B. Awerbuch, Y. Bartal, A. Fiat, and A. Rosén. Competitive Non-Preemptive Call Control. In Proc. 5th Annual ACM-SIAM Symp. on Discrete Algorithms, pages 312–320, 1994.Google Scholar
- 3.B. Awerbuch, R. Gawlick, T. Leighton, and Y. Rabani. On-line Admission Control and Circuit Routing for High Performance Computation and Communication. In 35th IEEE Symposium on Foundations of Computer Science, pages 412–423, 1994.Google Scholar
- 5.J. Boyar, K. S. Larsen, and M. N. Nielsen. The Accommodating Function — A Generalization of the Competitive Ratio. Tech. report 24, Department of Mathematics and Computer Science, University of Southern Denmark, Main Campus: Odense University, 1998. Extended version submitted for journal publication 1999.Google Scholar
- 7.E. G. Coffman, Jr., M. R. Garey, and D. S. Johnson. Approximation Algorithms for Bin Packing: A Survey. In Dorit S. Hochbaum, editor, Approximation Algorithms for NP-Hard Problems, chapter 2, pages 46–93. PWS Publishing Company, 1997.Google Scholar
- 11.A. Fiat. Personal communication, 1999.Google Scholar