Abstract
In the bin covering problem, given a list L = (a1,... , a n) of items with sizes sl(ai)∈ (0,1), the goal is to find a packing of the items into bins such that the number of bins that receive items of total size at least 1 is maximized. This is a dual problem to the classical bin packing problem. In this paper we present the first asymptotic fully polynomial-time approximation scheme (AFPTAS) for the bin covering problem.
Supported in part by EU Project APPOL I + II, Approximation and Online Algorithms, IST-1999-14084, and IST-2001-30012, by the EU Research Training Network ARACNE, Approximation and Randomized Algorithms in Communication Networks, HPRN-CT-1999-00112, and by the Natural Sciences and Engineering Research Council of Canada grant R3050A01.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S.B. Assman, D.S. Johnson, D.J. Kleitman and J.Y-T. Leung, On the dual of the one-dimensional bin packing problem, Journal on Algorithms 5 (1984), 502–525.
S.B. Assman, Problems in Discrete Applied Mathematics, PhD thesis, Department of Mathematics, MIT, Cambridge, MA, 1983.
J. Csirik, J.B.G. Frenk, M. Labbe and S. Zhang, Two simple algorithms for bin covering, Acta Cybernetica 14 (1999), 13–25.
J. Csirik, D.S. Johnson and C. Kenyon, Better approximation algorithms for bin covering, Proceedings of SI AM Conference on Discrete Algorithms (2001).
J. Csirik and V. Totik, On-line algorithms for a dual version of bin packing, Discrete Applied Mathematics, 21 (1988), 163–167.
W.F. de la Vega and C.S. Lueker, Bin packing can be solved within 1 + ∈ in linear time, Combinatorica, 1 (1981), 349–355.
M.D. Grigoriadis and L.G. Khachiyan, Fast approximation schemes for convex programs with many blocks and coupling constraints, SIAM Journal on Optimization, 4 (1994), 86–107.
M.D. Grigoriadis and L.G. Khachiyan, Coordination complexity of parallel price-directive decomposition, Mathematics of Operations Research, 21 (1996), pp. 321–340.
O.H. Ibarra and C.E. Kim, Fast approximation algorithms for the knapsack and sum of subset problem, Journal of the ACM, 22 (1975), 463–468.
K. Jansen and H. Zhang, Approximate algorithms for general packing problems with modified logarithmic potential function, to appear: Proceedings 2nd International Conference on Theoretical Computer Science, Montreal, 2002.
N. Karmarkar and R.M. Karp, An efficient approximation scheme for the one-dimensional bin packing problem, Proceedings 23rd Annual Symposium on Foundations of Computer Science (1982), 312–320.
H. Kellerer and U. Pferschy, A new fully polynomial approximation scheme for the knapsack problem, Proceedings 1st International Workshop on Approximation Algorithms for Combinatorial Optimization (1998), 123–134.
E. Lawler, Fast approximation algorithms for knapsack problems, Mathematics of Operations Research, 4 (1979), 339–356.
S.A. Plotkin, D.B. Shmoys, and E. Tardos, Fast approximation algorithms for fractional packing and covering problems, Mathematics of Operations Research, 20 (1995), 257–301.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jansen, K., Solis-Oba, R. (2002). An Asymptotic Fully Polynomial Time Approximation Scheme for Bin Covering. In: Bose, P., Morin, P. (eds) Algorithms and Computation. ISAAC 2002. Lecture Notes in Computer Science, vol 2518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36136-7_16
Download citation
DOI: https://doi.org/10.1007/3-540-36136-7_16
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00142-3
Online ISBN: 978-3-540-36136-7
eBook Packages: Springer Book Archive