An efficient fully polynomial approximation scheme for the Subset-Sum Problem

Journal of Computer and System Sciences

Volumn 66, Issue 2, 2003, Pages 349-370

  Kellerer, Hans ^a   Mansini, Renata ^b   Pferschy, Ulrich ^a   Speranza, Maria Grazia ^b  

^a UNIVERSITY OF GRAZ   (Austria)

^b UNIVERSITY OF BRESCIA   (Italy)

Author keywords

Fully polynomial approximation scheme; Knapsack problem; Subset sum problem; Worst case performance

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; ERROR ANALYSIS; OPTIMIZATION; PROBLEM SOLVING; SET THEORY;

APPROXIMATION ERROR; PROGRAM VERIFICATION; ROBUSTNESS AND STABILITY OF FUNCTIONAL EQUATIONS; SELF-TESTING PROGRAMS;

POLYNOMIAL APPROXIMATION;

EID: 15244364115     PISSN: 00220000     EISSN: 10902724     Source Type: Journal    
DOI: 10.1016/S0022-0000(03)00006-0     Document Type: Article

References (19)

1. R.E. Bellman, Dynamic Programming, Princeton University Press, Princeton, 1957.
2. V. Chvatal, Hard knapsack problems, Oper. Res. 28 (1980) 1402-1411.
3. D. Dor, U. Zwick, Selecting the median, in: Proceedings of the Sixth ACM-SIAM Symposium on Discrete Algorithms, 1995, pp. 28-35.
4. M.R. Garey, D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, 1979.
5. G.V. Gens, E.V. Levner, Approximation algorithms for certain universal problems in scheduling theory, Soviet J. Comput. System Sci. 6 (1978) 31-36.
6. G.V. Gens, E.V. Levner, Fast approximation algorithms for knapsack type problems, in: K. Iracki, K. Malinowski, S. Walukiewicz (Eds.), Optimization Techniques, Part 2, Lecture Notes in Control and Information Sciences, Vol. 74, Springer, Berlin, 1980, pp. 185-194.
7. G.V. Gens, E.V. Levner, A fast approximation algorithm for the subset-sum problem, INFOR 32 (1994) 143-148.
8. O.H. Ibarra, C.E. Kim, Fast approximation algorithms for the knapsack and sum of subset problems, J. ACM 22 (1975) 463-468.
9. D.S. Johnson, Approximation algorithms for combinatorial problems, J. Comput. System Sci. 9 (1974) 339-356.
10. R.M. Karp, The fast approximate solution of hard combinatorial problems, Proceedings of the Sixth Southeastern Conference on Combinatorics, Graph Theory, and Computing, Utilitas Mathematica Publishing, Winnipeg, 1975, pp. 15-31.
11. H. Kellerer, U. Pferschy, A new fully polynomial time approximation scheme for the knapsack problem, J. Combin. Optim. 3 (1999) 59-71.
12. H. Kellerer, U. Pferschy, Improved dynamic programming in connection with an FPTAS for the knapsack problem, J. Combin. Optim., to appear.
13. H. Kellerer, U. Pferschy, M.G. Speranza, An efficient fully polynomial approximation scheme for the subset-sum problem, Proceedings of the Eighth ISAAC Symposium, Springer Lecture Notes in Computer Science, Vol. 1350, Springer, Berlin, 1997, pp. 394-403.
14. E. Lawler, Fast approximation algorithms for knapsack problems, Math. Oper. Res. 4 (1979) 339-356.
15. M.J. Magazine, O. Oguz, A fully polynomial approximation algorithm for the 0-1 knapsack problem, European J. Oper. Res. 8 (1981) 270-273.
16. S. Martello, P. Toth, Worst-case analysis of greedy algorithms for the subset-sum problem, Math. Programming 28 (1984) 198-205.
17. S. Martello, P. Toth, Approximation schemes for the subset-sum problem: survey and experimental results, European J. Oper. Res. 22 (1985) 56-69.
18. S. Martello, P. Toth, Knapsack Problems: Algorithms and Computer Implementations, Wiley, Chichester, 1990.
19. D. Pisinger, Linear time algorithms for knapsack problems with bounded weight, J. Algorithms 33 (1999) 1-14.