SIGACT News Online Algorithms Column 26: Bin packing in multiple dimensions

I mentioned in a previous column [22] that the best known lower bound for the two-dimensional online bin packing problem is 1.907 by Blitz, van Vliet, Woeginger [2], which is an unpublished (and now lost [24]) manuscript. I have realized since then that even the penultimate result, 1.856, was published only in Andre van Vliet’s Ph.D. thesis [23] and is not readily available. It therefore seems like a good idea to describe his methods here, though not in full detail. This will include a discussion of the three-dimensional case. I will also survey other results in multidimensional packing, that were left out in my previous column. I would like to invite more contributions to this column, be it surveys, conference reports, or technical articles related to online algorithms and competitive analysis. If you are considering becoming a guest writer, don’t hesitate to mail me at rvs4@le.ac.uk.

[1]  Gerhard J. Woeginger,et al.  A Lower Bound for On-Line Vector-Packing Algorithms , 1993, Acta Cybern..

[2]  Yossi Azar,et al.  Tight bounds for online vector bin packing , 2013, STOC '13.

[3]  Edward G. Coffman,et al.  Dynamic, First-Fit Packings in Two or More Dimensions , 1984, Inf. Control..

[4]  Guochuan Zhang,et al.  Strip Packing vs. Bin Packing , 2006, AAIM.

[5]  Satoshi Fujita,et al.  Two-dimensional on-line bin packing problem with rotatable items , 2002, Theor. Comput. Sci..

[6]  G. Woeginger,et al.  Improved Lower Bounds for Online Hypercube and Rectangle Packing , 2016 .

[7]  L. Moser,et al.  On packing of squares and cubes , 1968 .

[8]  Guochuan Zhang,et al.  A new upper bound 2.5545 on 2D Online Bin Packing , 2011, TALG.

[9]  Edward G. Coffman,et al.  Dynamic Bin Packing , 1983, SIAM J. Comput..

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

[11]  Leah Epstein,et al.  Two-dimensional online bin packing with rotation , 2010, Theor. Comput. Sci..

[12]  Leah Epstein,et al.  Two Dimensional Packing: The Power of Rotation , 2003, MFCS.

[13]  Magnús M. Halldórsson,et al.  Lower bounds for on-line graph coloring , 1992, SODA '92.

[14]  Yoshiharu Kohayakawa,et al.  Multidimensional Cube Packing , 2001, Algorithmica.

[15]  János Csirik,et al.  An on-line algorithm for multidimensional bin packing , 1993, Oper. Res. Lett..

[16]  Rob van Stee,et al.  SIGACT news online algorithms column 20: the power of harmony , 2012, SIGA.

[17]  Leah Epstein,et al.  Dynamic multi-dimensional bin packing , 2010, J. Discrete Algorithms.

[18]  Andrew Chi-Chih Yao,et al.  Resource Constrained Scheduling as Generalized Bin Packing , 1976, J. Comb. Theory A.

[19]  Rob van Stee,et al.  New bounds for multi-dimensional packing , 2002, SODA '02.

[20]  Yong Zhou,et al.  A note on online hypercube packing , 2010, Central Eur. J. Oper. Res..

[21]  Rob van Stee,et al.  New Bounds for Multidimensional Packing , 2003, Algorithmica.

[22]  Kam-Hoi Cheng,et al.  Heuristic Algorithms for On-Line Packing in Three Dimensions , 1992, J. Algorithms.

[23]  Leah Epstein,et al.  Online square and cube packing , 2005, Acta Informatica.