An efficient parallel algorithm for solving the Knapsack problem on hypercubes

Journal of Parallel and Distributed Computing

Volumn 64, Issue 11, 2004, Pages 1213-1222

  Goldman, Alfredo ^a   Trystram, Denis ^a  

^a ID IMAG   (France)

Author keywords

Hypercube; Irregular mesh; Knapsack problem; Scheduling

Indexed keywords

COMPUTATIONAL METHODS; CONSTRAINT THEORY; DYNAMIC PROGRAMMING; FUNCTION EVALUATION; GRAPH THEORY; ITERATIVE METHODS; MATHEMATICAL MODELS; PARALLEL ALGORITHMS; SCHEDULING; SET THEORY;

HYPERCUBES; IRREGULAR MESH; KNAPSACK PROBLEM; SCHEDULING ALGORITHM;

PROBLEM SOLVING;

EID: 7544232505     PISSN: 07437315     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jpdc.2002.10.001     Document Type: Article

References (28)

1. V. Aleksandrov, S. Fidanova, Non-uniform recurrence equations on 2d regular arrays, in: Advance in Numerical Methods and Applications, in Proceedings of NMA94, August 1994, pp. 217-225.
2. V. Aleksandrov, S. Fidanova, On the expected execution time for a class of non uniform recurrence equations mapped onto Id array, Parallel Algorithms Appl. 1 (1994) 303-314.
3. R. Andonov, F. Gruau, A 2D modular toroidal systolic array for the Knapsack problem, in: ASAP'91, 1991, pp. 458-472.
4. R. Andonov, V. Poirriez, S. Rajopadhye, Unbounded Knapsack problem: dynamic programming revisited, European J. Oper. Res. 123 (2000) 394-407.
5. R. Andonov, P. Quinton, Efficient linear systolic array for Knapsack problem, CONPAR'92, Lecture Notes in Computer Science, vol. 634, Springer, Berlin, 1992, pp. 247-258.
6. R. Andonov, S. Rajopadhye, Knapsack on VLSI: from algorithm to optimal circuits, IEEE Trans. Parallel Distributed Systems 8 (6) (1997) 545-562.
7. E. Bampis, J-C. König, C. Delorme, Optimal schedule for d-d grid graphs with communication delays, Parallel Computing 24 (11) (1998) 1653-1664.
8. G-H. Chen, M-S. Chern, J-H. Jang, Pipeline architectures for dynamic programming algorithms, Parallel Comput. 13 (1) (1990) 111-117.
9. G-H. Chen, J-H. Jang, An improved parallel algorithm for 0/1 knapsack problem, Parallel Comput. 18 (7) (1992) 811-821.
10. E.G. Coffman, P.J. Denning, Operating Systems Theory, Prentice-Hall Series in Automatic Computation, 1973.
11. E.G. Coffman, M.R. Garey, D.S. Johnson, A.S. Lapaugh, Scheduling file transfers, SIAM J. Comput. 14 (3) (August 1985) 744-780.
12. M. Cosnard, A. Ferreira, H. Herbelin, The two list algorithm for the Knapsack problem on a FPS T20, Parallel Comput. 3 (9) (1988/1989) 385-388.
13. M.R. Garey, D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness, W.H. Freeman and Company, San Francisco, 1979.
14. T. Gerasch, P. Wang, Implementing dynamic programming on the connection machine, Technical Report Series TR-10-89, George Mason University, 1989.
15. T. Gerasch, P. Wang, A survey of parallel algorithm for one-dimensional integer Knapsack problems, Infor 32 (3) (1993) 163-186.
16. A. Goldman, D. Trystram, An efficient parallel algorithm for solving the Knapsack problem on hypercube, in: 11th International Parallel Processing Symposium, April 1997, pp. 608-615.
17. E. Horowitz, S. Sahni, Computing partitions with applications to the Knapsack problem, J. ACM 21 (1974) 277-292.
18. T.C. Hu, Combinatorial algorithms, Addison-Wesley, Reading, MA, 1982.
19. E. Karnin, A parallel algorithm for the Knapsack problem, IEEE Trans. Comput. 33 (5) (1984) 404-408.
20. J. Lee, E. Shragowitz, S. Sahni, A hypercube algorithm for the 0/1 Knapsack problem, J. Parallel Distributed Comput. 5 (4) (1988) 438-456.
21. F. Leighton, Parallel Algorithms and Architectures: ArraysTrees-Hypercubes, Morgan Kaufmann, Los Altos, CA, 1992.
22. J. Lin, J. Storer, Processor efficient hypercube algorithm for the Knapsack problem, J. Parallel Distributed Comput. 13 (3) (1991) 332-337.
23. S. Martello, P. Toth, Knapsack Problems: Algorithms and Computer Implementations, Wiley, New York, London, Sydney, 1990.
24. D.G. Morales, F. Almeida, C. Rodríguez, J.L. Roda, I. Coloma, A. Delgado, Parallel dynamic programming and automata theory, Parallel Comput. 26 (2000) 113-134.
25. C. Picouleau, New complexity results on scheduling with small communication delays, J. Discrete Appl. Math. 60 (1995) 331-342.
26. D. Pisinger, A minimal algorithm for the 0-1 Knapsack problem, Oper. Res. 45 (5) (September-October 1997) 758-767.
27. S. Teng, Adaptive parallel algorithms for integral Knapsack problems, J. Parallel Distributed Comput. 8 (1990) 400-406.
28. N. Zhu, K. Broughan, On dominated terms in the general Knapsack problem, Oper. Res. Lett. 21 (1997) 31-37