Abstract
In this paper, we look at the online bounded-space bin cover problem and show how we can use the language of Markov chains to model and analyze the problem. We will use the insights given by the Markov chains to design an algorithm for the online bounded-space bin cover problem. The algorithm is a heuristic that we create by simplifying the Markov chain. We also show how we can use simple methods to improve the efficiency of the algorithm. Finally, we will analyze our algorithm and compare it to a well known online bin cover algorithm.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Asgeirsson, E. I., & Stein, C. (2006). Using Markov chains to design algorithms for on-line bounded-space bin-cover. In Proceedings of the ACM-SIAM workshop on algorithm engineering and experiments (pp. 75–85).
Assman, A. B., Johnson, D. J., Kleitman, D. J., & Leung, J. Y.-T. (1984). On a dual version of the one-dimensional bin packing problem. Journal of Algorithms, 5, 502–525.
Coffman, E. G. Jr., & Lueker, G. S. (1991). An introduction to the probabilistic analysis of packing and partitioning algorithms. New York: Wiley.
Coffman, E. G. Jr., Johnson, D. S., Shor, P. W., & Weber, R. R. (1993). Markov chains, computer proofs, and average-case analysis of best fit bin packing. In STOC ’93: Proceedings of the twenty-fifth annual ACM symposium on theory of computing (pp. 412–421).
Coffman, E. G. Jr., Courcoubetis, C., Garey, M. R., Johnson, D. S., Shor, P. W., Weber, R. R., & Yannakakis, M. (2002). Perfect packing theorems and the average case behavior of optimal and on-line packings. SIAM Review, 44, 384–402.
Courcoubetis, C., & Weber, R. R. (1990). Stability of on-line bin packing with random arrivals and long-run average constraints. Probability in the Engineering and Informational Sciences, 4, 447–460.
Csirik, J., & Totik, V. (1988). Online algorithms for a dual version of bin packing. Discrete Applied Mathematics, 21(2), 163–167.
Csirik, J., Frenk, J. B. G., Galambos, G., & Rinooy Kan, A. H. G. (1991). Probabilistic analysis of algorithms for dual bin packing problems. Journal of Algorithms, 12(2), 189–203.
Csirik, J., Johnson, D. S., Kenyon, C., Shor, P. W., & Weber, R. R. (1999). A self organizing bin packing heuristic. In Proceedings of the workshop on algorithmic engineering and experimentation (ALENEX ’99) (pp. 246–265).
Csirik, J., Johnson, D. S., Kenyon, C., Orlin, J. B., Shor, P. W., & Weber, R. R. (2000). On the sum-of-squares algorithm for bin packing. In Proceedings of the 32nd annual ACM symposium on theory of computing (pp. 208–217).
Csirik, J., Johnson, D., & Kenyon, C. (2001). Better approximation algorithms for bin covering. In Proceedings of the 12th ACM-SIAM symposium on discrete algorithms (pp. 557–566).
de la Vega, W. F., & Lueker, G. S. (1981). Bin packing can be solved within 1+ε in linear time. Combinatorica, 1(4), 349–355.
Jensson, P., Jonsson, M. T., & Runarsson, T. P. (1996). Dynamic dual bin packing using fuzzy objectives. In Proceedings of 1996 IEEE international conference on evolutionary computation (ICEC ’96) (pp. 219–222).
Karmarkar, N., & Karp, R. (1982). An efficient approximation scheme for the one-dimensional bin-packing problem. In Proceedings of the 23rd annual symposium on foundations of computer science (pp. 312–320).
Ross, S. M. (2000). Introduction to probability models. San Diego: Academic Press.
Author information
Authors and Affiliations
Corresponding author
Additional information
A preliminary version of this paper appeared in the proceedings of ALENEX 2006 (Asgeirsson and Stein 2006).
Rights and permissions
About this article
Cite this article
Asgeirsson, E.I., Stein, C. Bounded-space online bin cover. J Sched 12, 461–474 (2009). https://doi.org/10.1007/s10951-009-0116-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10951-009-0116-x