Abstract
We are concerned with a variant of the classical one‐dimensionalbin‐packing problem. n items have to be packed into unit‐capacity bins such that the total number of used bins isminimized with the additional constraint that at most k items can beassigned to one bin. In 1975, Krause et al. analyzed several approximation algorithms forthis problem and showed that they all have an asymptotic worst‐case performance ratioof 2. No better algorithms have been found so far. We present a new heuristic with anasymptotic worst-case bound of 3/2 and O(n log2 n)running time.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. Babel and H. Kellerer, An on-line algorithm for cardinality constrained bin packing problems, Technical Report 6/1998, Faculty of Economics, University of Graz, submitted.
E.G. Coffman, M.R. Garey and D.S. Johnson, Approximation algorithms for bin-packing — an updated survey, in: Analysis and Design of Algorithms in Combinatorial Optimization, eds. Ausiello and Lucertini, Springer, New York, 1984, pp. 49-106.
W. Fernandez de la Vega and G.S. Luecker, Bin packing can be solved within 1 + ɛ in linear time, Combinatorica 1(1981)349-355.
G. Galambos and G.J. Woeginger, On-line bin packing — a restricted survey, ZOR — Mathematical Methods of Operations Research 42(1995)25-45.
M.R. Garey, R.L. Graham, D.S. Johnson and A.C. Yao, Resource constrained scheduling as generalized bin packing, J. Combinatorial Theory Ser. A21(1976)257-298.
D.S. Johnson, Near-optimal bin packing algorithms, Doctoral Thesis, MIT, Cambridge, MA, 1973.
D.S. Johnson, A. Demers, J.D. Ullman, M.R. Garey and R.L. Graham, Worst-case performance bounds for simple one-dimensional packing algorithms, SIAM Journal of Computing 3(1974)299-325.
K.L. Krause, V.Y. Shen and H.D. Schwetman, Analysis of several task-scheduling algorithms for a model of multiprogramming computer systems, Journal of the ACM 22(1975)522-550.
K.L. Krause, V.Y. Shen and H.D. Schwetman, Analysis of several task-scheduling algorithms for a model of multiprogramming computer systems, Errata, Journal of the ACM 24(1977)527.
Rights and permissions
About this article
Cite this article
Kellerer, H., Pferschy, U. Cardinality constrained bin‐packing problems. Annals of Operations Research 92, 335–348 (1999). https://doi.org/10.1023/A:1018947117526
Issue Date:
DOI: https://doi.org/10.1023/A:1018947117526