Online bin packing with resource augmentation

In competitive analysis, we usually do not put any restrictions on the computational complexity of online algorithms, although efficient algorithms are preferred. Thus, if such an algorithm were given the entire input in advance, it could give an optimal solution (in exponential time). Instead of giving the algorithm more knowledge about the input, in this paper we consider the effects of giving an online bin packing algorithm larger bins than the offline algorithm it is compared to. We give new algorithms for this problem that combine items in bins in an unusual way, and give bounds on their performance which improve upon the best possible bounded space algorithm. We also give general lower bounds for this problem which are nearly matching for bin sizes b>=2.

[1]  D. T. Lee,et al.  A simple on-line bin-packing algorithm , 1985, JACM.

[2]  D. T. Lee,et al.  On-Line Bin Packing in Linear Time , 1989, J. Algorithms.

[3]  David S. Johnson,et al.  Fast Algorithms for Bin Packing , 1974, J. Comput. Syst. Sci..

[4]  Cynthia A. Phillips,et al.  Optimal Time-Critical Scheduling via Resource Augmentation , 1997, STOC '97.

[5]  Gerhard J. Woeginger,et al.  On-line Packing and Covering Problems , 1996, Online Algorithms.

[6]  Edward G. Coffman,et al.  Approximation algorithms for bin packing: a survey , 1996 .

[7]  André van Vliet,et al.  An Improved Lower Bound for On-Line Bin Packing Algorithms , 1992, Inf. Process. Lett..

[8]  Jeffrey D. Ullman,et al.  The performance of a memory allocation algorithm , 1971 .

[9]  Bala Kalyanasundaram,et al.  Speed is as powerful as clairvoyance , 2000, JACM.

[10]  Vijay V. Vazirani,et al.  Approximation Algorithms , 2001, Springer Berlin Heidelberg.

[11]  Jeffrey D. Ullman,et al.  Worst-case analysis of memory allocation algorithms , 1972, STOC.

[12]  Leah Epstein,et al.  New Bounds for Variable-Sized and Resource Augmented Online Bin Packing , 2002, ICALP.

[13]  Donna J. Brown,et al.  A Lower Bound for On-Line One-Dimensional Bin Packing Algorithms. , 1979 .

[14]  Steven S. Seiden,et al.  On the online bin packing problem , 2001, JACM.

[15]  János Csirik,et al.  Resource augmentation for online bounded space bin packing , 2000, J. Algorithms.

[16]  Frank M. Liang.  A Lower Bound for On-Line Bin Packing , 1980, Inf. Process. Lett..