Approximate strip packing: Revisited

In this paper we establish an algorithmic framework between bin packing and strip packing, with which strip packing can be very well approximated by applying some bin packing algorithms. More precisely we obtain the following results: (1) Any off-line bin packing algorithm can be applied to strip packing maintaining almost the same asymptotic worst-case ratio. (2) A class of Harmonic-based algorithms for bin packing, such as Refined Harmonic, Modified Harmonic, Harmonic++, can be applied to online strip packing. In particular, we show that online strip packing admits an upper bound of 1.58889 + ź on the asymptotic competitive ratio, for any arbitrarily small ź 0 . This significantly improves the previously best bound of 1.6910 and affirmatively answers an open question posed by Csirik and Woeginger (1997). Moreover, the time complexity mainly depends on a sorting procedure and the bin packing algorithms employed.

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

[2]  Richard M. Karp,et al.  An efficient approximation scheme for the one-dimensional bin-packing problem , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[3]  Igal Golan,et al.  Performance Bounds for Orthogonal Oriented Two-Dimensional Packing Algorithms , 1981, SIAM J. Comput..

[4]  Gerhard J. Woeginger,et al.  Shelf Algorithms for On-Line Strip Packing , 1997, Inf. Process. Lett..

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

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

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

[8]  Claire Mathieu,et al.  A Near-Optimal Solution to a Two-Dimensional Cutting Stock Problem , 2000, Math. Oper. Res..

[9]  Brenda S. Baker,et al.  A 5/4 Algorithm for Two-Dimensional Packing , 1981, J. Algorithms.

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

[11]  D. Simchi-Levi.  New worst‐case results for the bin‐packing problem , 1994 .

[12]  Brenda S. Baker,et al.  A New Proof for the First-Fit Decreasing Bin-Packing Algorithm , 1985, J. Algorithms.

[13]  M. Yue,et al.  A simple proof of the inequality MFFD(L)≤71/60 OPT(L) + 1,L for the MFFD bin-packing algorithm , 1991 .

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

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

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

[17]  Robert E. Tarjan,et al.  Performance Bounds for Level-Oriented Two-Dimensional Packing Algorithms , 1980, SIAM J. Comput..

[18]  Brenda S. Baker,et al.  Shelf Algorithms for Two-Dimensional Packing Problems , 1983, SIAM J. Comput..