Computing Partitions with Applications to the Knapsack Problem

Journal of the ACM (JACM)

Volumn 21, Issue 2, 1974, Pages 277-292

  Horowitz, Ellis ^a   Sahni, Sartaj ^a,b  

^a Cornell University ^*  (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

dynamic programming; integer optimization; knapsack problem; partitions

Indexed keywords

MATHEMATICAL PROGRAMMING, DYNAMIC;

EID: 0016047180     PISSN: 00045411     EISSN: 1557735X     Source Type: Journal    
DOI: 10.1145/321812.321823     Document Type: Article

References (15)

1. Beckenbach, E. F. (Ed). Applied Combinatorial Mathematics. Wiley, New York, 1964.
2. Bradlky, G. H. Transformation of integer programs to knapsack problems. Discrete Math 1, 1 (May 1971), 29-45.
3. Cook, Stephen A. The complexity of theorem proving procedures. Conf. Record of Third ACM Symposium on Theory of Computing, 1970, pp. 151-158.
4. Gilmore, P. C., and Gomory, R. E. Multistage cutting stock problems of two and more dimensions. Oper. Res. 13 (1965), 94-120.
5. Gilmore, P. C., and Gomoby, R. E. The theory and computation of knapsack functions. Oper. Res. 14, (1966), 1045-1074.
6. Greenberg, H., and Hegerich, R. L. A branch search algorithm for the knapsack problem. Manage. Sci. 16, 5 (Jan. 1970), 327-332.
7. Hardy, G. H., and Wright, E. M. An Introduction to the Theory of Numbers, 4th ed. Clarendon Press, Oxford, England, 1959.
8. Ingargiola, G. P., and Korsh, J. F. A reduction algorithm for zero-one single knapsack problems. Manage. Sci. (to appear).
9. Karp, R. Reducibility among combinatorial problems. In Complexity of Computer Computations, R. E. Miller and J. W. Thather, Eds., Plenum Press, N. Y., 1972, pp. 85-104.
10. Kolesar, P. J. A branch and bound algorithm for the knapsack problem. Manage. Sci. 13 (May 1967), 723-735.
11. Lawler, E. L., and Bull, M. D. A method for solving discrete optimisation problems. Oper. Res. 14 (1966), 1098-1112.
12. Musser, David R. Algorithms for polynomial factorization. Ph.D. Th., T.R. # 134, Computer Sciences Dep., U. of Wisconsin, Sept. 1971.
13. Nemhauser, G. L., and Ullman, Z. Discrete dynamic programming and capital allocation. Manage. Sci. 15, 9 (May 1969), 494-505.
14. Nemhauser, G. L., and Garfinkel, R. Integer Programming. Wiley, New York, 1972.
15. Weingartner, H. Martin, and Ness, David N. Methods for the solution of the multi-dimensional 0/1 knapsack problem. Oper. Res. 15, 1 (Jan.-Feb. 1967), 83-103.