The class constrained bin packing problem with applications to video-on-demand

In this paper we present approximation results for the class constrained bin packing problem that has applications to Video-on-Demand Systems. In this problem we are given bins of size B with C compartments, and n items of Q different classes, each item i@?{1,...,n} with class c"i and size s"i. The problem is to pack the items into bins, where each bin contains at most C different classes and has total items size at most B. We present several approximation algorithms for offline and online versions of the problem.

[1]  Eduardo C. Xavier,et al.  A one-dimensional bin packing problem with shelf divisions , 2008, Discret. Appl. Math..

[2]  Hadas Shachnai,et al.  Multiprocessor Scheduling with Machine Allotment and Parallelism Constraints , 2002, Algorithmica.

[3]  Dorit S. Hochbaum,et al.  Approximation Algorithms for NP-Hard Problems , 1996 .

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

[5]  János Csirik,et al.  The Parametric Behavior of the First-Fit Decreasing Bin Packing Algorithm , 1993, J. Algorithms.

[6]  Eduardo C. Xavier,et al.  Approximation schemes for knapsack problems with shelf divisions , 2006, Theor. Comput. Sci..

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

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

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

[10]  Hadas Shachnai,et al.  On Two Class-Constrained Versions of the Multiple Knapsack Problem , 2001, Algorithmica.

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

[12]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[13]  Shahram Ghandeharizadeh,et al.  Design and Implementation of Scalable Continuous Media Servers , 1998, Parallel Comput..

[14]  Hadas Shachnai,et al.  Tight bounds for online class-constrained packing , 2002, Theor. Comput. Sci..

[15]  Yoshiko Wakabayashi,et al.  Parametric on-line algorithms for packing rectangles and boxes , 2003, Eur. J. Oper. Res..

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

[17]  Philip S. Yu,et al.  Disk load balancing for video-on-demand systems , 1997, Multimedia Systems.

[18]  Tami Tamir,et al.  Polynominal time approximation schemes for class-constrained packing problem , 2000, APPROX.

[19]  Samir Khuller,et al.  Approximation algorithms for data placement on parallel disks , 2000, SODA '00.

[20]  Hadas Shachnai,et al.  Approximation Schemes for Generalized 2-Dimensional Vector Packing with Application to Data Placement , 2003, RANDOM-APPROX.

[21]  Ann L. Chervenak,et al.  Tertiary Storage: An Evaluation of New Applications , 1994 .

[22]  Zeger Degraeve,et al.  The Co-Printing Problem: A Packing Problem with a Color Constraint , 2004, Oper. Res..

[23]  Samir Khuller,et al.  Algorithms for non-uniform size data placement on parallel disks , 2003, J. Algorithms.

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

[25]  Milind Dawande,et al.  The Surplus Inventory Matching Problem in the Process Industry , 2000, Oper. Res..

[26]  Milind Dawande,et al.  Variable Sized Bin Packing With Color Constraints , 2001, Electron. Notes Discret. Math..

[27]  G. S. Lueker,et al.  Bin packing can be solved within 1 + ε in linear time , 1981 .

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