On the Sum-of-Squares algorithm for bin packing

Journal of the ACM

Volumn 53, Issue 1, 2006, Pages 1-65

  Csirik, Janos ^a   Johnson, David S ^b   Kenyon, Claire ^c,f   Orlin, James B ^d,g   Shor, Peter W ^d   Weber, Richard R ^e  

^a UNIVERSITY OF SZEGED   (Hungary)

^b AT AND T LABS RESEARCH   (United States)

^c BROWN UNIVERSITY   (United States)

^d MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^e UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^f Brown Univerity   (United States)

^g MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Approximation algorithms; Average case analysis; Bin packing

Indexed keywords

ALGORITHMS; LINEAR PROGRAMMING; OPTIMAL CONTROL SYSTEMS; PROBLEM SOLVING;

AVERAGE CASE ANALYSIS; BIN PACKING; PSEUDOPOLYNOMIAL-TIME ALGORITHM;

LEAST SQUARES APPROXIMATIONS;

EID: 33745222500     PISSN: 00045411     EISSN: 00045411     Source Type: Journal    
DOI: 10.1145/1120582.1120583     Document Type: Article

References (31)

1. ALBERS, S., AND MITZENMACHER, M. 1998. Average-case analyses of first fit and random fit bin-packing. In Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms. SIAM, Philadelphia, PA, 290-299.
2. ALON, N., AND SPENCER, J. H. 1992. The Probabilistic Method. Wiley Interscience, New York, NY.
3. APPLEGATE, D. L., BURIOL, L., DILLARD, B., JOHNSON, D. S., AND SHOR, P. W. 2003. The cutting-stock approach to bin-packing: Theory and experiments. In Proceedings of the 5th Workshop on Algorithm Engineering and Experimentation. SIAM, Philadelphia, PA, 1-15.
4. COFFMAN, JR., E. G., COURCOUBETIS, C., GAREY, M. R., JOHNSON, D. S., MCGEOCH, L. A., SHOR, P. W., WEBER, R. R., AND YANNAKAKIS, M. 1991. Fundamental discrepancies between average-case analyses under discrete and continuous distributions. InProceedings of the 23rd Annual ACM Symposium on Theory of Computing. ACM, New York, 230-240.
5. COFFMAN, JR., E. G., COURCOUBETIS, C., GAREY, M. R., JOHNSON, D. S., SHOR, P. W., WEBER, R. R., AND YANNAKAKIS, M. 2000. Bin packing with discrete item sizes, Part I: Perfect packing theorems and the average case behavior of optimal packings. SIAM J. Disc. Math. 13, 384-402.
6. COFFMAN, JR., E. G., COURCOUBETIS, C., GAREY, M. R., JOHNSON, D. S., SHOR, P. W., WEBER, R. R., AND YANNAKAKIS, M. 2002. Perfect packing theorems and the average-case behavior of optimal and online bin-packing. SIAM Review 44, 95-108. (Updated version of Coffman, Jr. et al. [2000]).
7. COFFMAN, JR., E. G., JOHNSON, D. S., MCGEOCH, L. A., SHOR, P. W., AND WEBER, R. R. 2005 Bin packing with discrete item sizes, Part III: Average case behavior of FFD and BFD. In preparation.
8. COFFMAN, JR., E. G., JOHNSON, D. S., SHOR, P. W., AND WEBER, R. R. 1993. Markov chains, computer proofs, and average-case analysis of Best Fit bin-packing. In Proceedings of the 25th Annual ACM Symposium on Theory of Computing. ACM, New York, 412-421.
9. COFFMAN, JR., E. G., JOHNSON, D. S., SHOR, P. W., AND WEBER, R. R. 1997. Bin packing with discrete item sizes, Part II: Tight bounds on first fit. Rand. Struct. Alg. 10, 69-101.
10. COURCOUBETIS, C., AND WEBER, R. R. 1990. Stability of online bin-packing with random arrivals and long-run average constraints. Prob. Eng. Inf. Sci. 4, 447-460.
11. CSIRIK, J., JOHNSON, D. S., AND KENYON:, C. 2001. Better approximation algorithms for bin covering. In Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms. SIAM, Philadelphia, PA, 557-566.
12. CSIRIK, J., JOHNSON, D. S., AND KENYON, C. 2005. On the worst-case performance of the sum-of-squares algorithm for bin-packing. E-Print arXiv:cs.DS/0509031, arXiv.org e-Print archive (http://arxiv.org/archive/cs).
13. CSIRIK, J., JOHNSON, D. S., KENYON, C., SHOR, P. W., AND WEBER, R. R. 1999. A self organizing bin-packing heuristic. In Proceedings 1999 Workshop on Algorithm Engineering and Experimentation, M. Goodrich and C. C. McGeoch, Eds. Lecture Notes in Computer Science, vol. 1619, Springer-Verlag, Berlin, Germany, 246-265.
14. GAREY, M. R., AND JOHNSON, D. S. 1979. Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, New York.
15. GILMORE, P. C., AND GOMORY, R. E. 1961. A linear programming approach to the cutting stock problem. Oper. Res. 9, 849-859.
16. GILMORE, P. C., AND GOMORY, R. E. 1963. A linear programming approach to the cutting stock program - Part II. Oper. Res. 11, 863-888.
17. GRÖTSCHEL, M., LOVASZ, L., AND SCHRIJVER, A. 1981. The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1, 169-197.
18. HAJEK, B. 1982. Hitting-time and occupation-time bounds implied by drift analysis with applications. Adv. Appl. Prob. 14, 502-525.
19. JOHNSON, D. S., DEMERS, A., ULLMAN, J. D., GAREY, M. R., AND GRAHAM, R. L. 1974. Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM J. Comput. 3, 299-325.
20. KARMARKAR, N., AND KARP, R. M. 1982. An efficient approximation scheme for the one-dimensional bin-packing problem. In Proceedings of the 23rd Annual IEEE Symposium on Foundations of Computer Science. IEEE Computer Society, Los Alamitos, Calif., 312-320.
21. KARP, R. M., AND PAPADIMITRIOU, C. H. 1982. On the linear characterization of combinatorial optimization problems. SIAM J. Comput. 11, 620-632.
22. KENYON, C., AND MITZENMACHER, M. 2002. Linear waste of best fit bin-packing on skewed distributions. Random Structures and Algorithms 20, 441-464.
23. (Preliminary version in Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science. IEEE Computer Society, Las Alamitos, CA, 2000, 582-589.)
24. KENYON, C., RABANI, Y., AND SINCLAIR, A. 1998. Biased random walks, Lyapunov functions, and stochastic analysis of best fit bin-packing. J. Algorithms 27, 218-235.
25. (Preliminary version in Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms. SIAM, Philadelphia, PA, 1996, 351-358.)
26. RHEE, W. T. 1988. Optimal bin-packing with items of random sizes. Math. Oper. Res. 13, 140-151.
27. RHEE, W. T., AND TALAGRAND, M. 1993a. On line bin-packing with items of random size. Math. Oper. Res. 18, 438-445.
28. RHEE, W. T., AND TALAGRAND, M. 1993b. On line bin-packing with items of random sizes - II. SIAM J. Comput. 22, 1251-1256.
29. VAIDYA, P. M. 1989. Speeding-up linear programming using fast matrix multiplication. In Proceedings of the 30th Annual IEEE Symposium on Foundations of Computer Science. IEEE Computer Society, Los Alamitos, CA, 332-337.
30. VALÉRIO DE CARVALHO, J. M. 1999. Exact solutions of bin-packing problems using column generation and branch and bound. Ann. Oper. Res. 86, 629-659.
31. VAN VLIET, A. 1992. An improved lower bound for online bin-packing algorithms. Inf. Proc. Lett. 43, 277-284.