The DOI matches its Crossref record; 5 of the 5 references it cites were found in a registry or an index.
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Open accessAbstract
Given a positive integer M and n pairs of positive integers (p~, cD, , (p. , c.), maximize the sum~ ~p~ subject to the constramts~ ~c, < M and ~, = 0 or 1 This is the well-known 0/1 knapsack problem An algorithm is presented which finds for any 0 < e < 1 an approximate solution P satisfying (P* -P)/P* < ~, where P* is the desired optimal sum Moreover, for any fixed e, the algorithm has time complexity 0(n log n) and space complexity O(n) Modification of the algorithm for the unbounded knapsack problem where the ~,'s can be any nonnegative integer results in a O(n) computing time A hnear-time algorithm is also obtained for a special class of 0/1 knapsack problems having the property that p,/c, is the same for all 1 < z < n KEY WORDS AND PHRASES.knapsack problem, sum of subset problem, P-complete problem, polynomial time algorithm, approximation algorithm CR CATEGORIES. 5 25, 5.39, 5 42
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Cites
Reducibility among Combinatorial Problems
Karp, R. M. (1972) · Complexity of Computer Computations · doi:10.1007/978-1-4684-2001-2_9 · Cited by 11,511
The complexity of theorem-proving procedures
Cook, S. A. (1971) · Proceedings of the third annual ACM symposium on Theory of computing - STOC '71 · doi:10.1145/800157.805047 · Cited by 6,385
Computing Partitions with Applications to the Knapsack Problem
Horowitz, E., & Sahni, S. K. (1974) · Journal of the ACM · doi:10.1145/321812.321823 · Cited by 605
Approximate Algorithms for the 0/1 Knapsack Problem
Sahni, S. (1975) · Journal of the ACM · doi:10.1145/321864.321873 · Cited by 349
Approximation algorithms for combinatorial problems
Johnson, D. S. (1973) · Proceedings of the fifth annual ACM symposium on Theory of computing - STOC '73 · doi:10.1145/800125.804034 · Cited by 272
Cited by
The Design of Approximation Algorithms
Williamson, D. P., & Shmoys, D. B. (2011) · Cambridge University Press eBooks · doi:10.1017/cbo9780511921735 · Cited by 1,301
Hiding information and signatures in trapdoor knapsacks
Merkle, R., & Hellman, M. (1978) · IEEE Transactions on Information Theory · doi:10.1109/tit.1978.1055927 · Cited by 827
A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem
Chekuri, C., & Khanna, S. (2005) · SIAM Journal on Computing · doi:10.1137/s0097539700382820 · Cited by 332
Computational Complexity of Discrete Optimization Problems
Lenstra, J. K., & Rinnooy Kan, A. H. G. (1979) · Annals of Discrete Mathematics · doi:10.1016/s0167-5060(08)70821-5 · Cited by 292
Dalyac, C., Henriet, L., Jeandel, E., Lechner, W., Perdrix, S., Porcheron, M., & Veshchezerova, M. (2021) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-021-00100-3 · Cited by 46
Metadata
- Authors
- Ibarra, O. H., & Kim, C. E.
- Venue
- Journal of the ACM
- Published
- 1975-10
- Volume
- 22
- Issue
- 4
- Pages
- 463-468
- ISSN
- 0004-5411 (ISSN-L)
- 1557-735X
- OpenAlex
- W2026891055
- Cited by
- 959
- References
- 5
- FWCI
- 89.80
- Type
- journal article
- Language
- en
- Open access
- bronze
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