An Optimal Online Algorithm for Bounded Space Variable-Sized Bin Packing

An online algorithm for variable-sized bin packing, based on the HARMONIC algorithm of Lee and Lee [11], is investigated. This algorithm is based on one proposed by Csirik [4]. It is shown that the algorithm is optimal among those which use bounded space. An interesting feature of the analysis is that, although it is shown that our algorithm achieves a performance ratio arbitrarily close to the optimum value, it is not known precisely what that value is. The case where bins of capacity 1 and α ∈ (0, 1) are used is studied in greater detail. It is shown that among algorithms which are allowed to chose α, the optimal performance ratio lies in [1.37530, 1.37532].

[1]  Gerhard J. Woeginger.  Improved Space for Bounded-Space, On-Line Bin-Packing , 1993, SIAM J. Discret. Math..

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

[3]  Jeffrey D. Ullman,et al.  Worst-Case Performance Bounds for Simple One-Dimensional Packing Algorithms , 1974, SIAM J. Comput..

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

[5]  Michael A. Langston,et al.  Online variable-sized bin packing , 1989, Discret. Appl. Math..

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

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

[8]  Michael A. Langston,et al.  A Storage-Size Selection Problem , 1984, Inf. Process. Lett..

[9]  Andrew Chi-Chih Yao,et al.  New Algorithms for Bin Packing , 1978, JACM.

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

[11]  Guochuan Zhang,et al.  Bounded Space On-Line Variable-Sized Bin Packing , 1997, Acta Cybern..

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

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

[14]  Steven S. Seiden.  On the Online Bin Packing Problem , 2001, ICALP.

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

[16]  David S. Johnson,et al.  Near-optimal bin packing algorithms , 1973 .

[17]  Michael B. Richey,et al.  Improved bounds for harmonic-based bin packing algorithms , 1991, Discret. Appl. Math..

[18]  D. K. Friesen,et al.  Variable Sized Bin Packing , 1986, SIAM J. Comput..