Greedy algorithms for the minimization knapsack problem: Average behavior

Journal of Computer and Systems Sciences International

Volumn 47, Issue 1, 2008, Pages 14-24

  Diubin, G N ^a   Korbut, A A ^a  

^a Institute for Economics and Mathematics   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DISTRIBUTED COMPUTER SYSTEMS; FUNCTION EVALUATION; OPTIMIZATION;

GREEDY ALGORITHMS; MINIMIZATION PROBLEM;

PROBLEM SOLVING;

EID: 40749153989     PISSN: 10642307     EISSN: None     Source Type: Journal    
DOI: 10.1134/s1064230708010036     Document Type: Article

References (20)

1. S. S. Skiena, "Who Is Interested in Algorithms and Why?-Lessons from the Stony Brook Algorithms Repository," in Proceedings of the Second Workshop on Algorithm Engineering (WAE'98), Saarbrücken, Germany, 1998, pp. 204-212.
2. H. Kellerer, U. Pferschy, and D. Pisinger, Knapsack Problems (Springer, Berlin, 2004).
3. M. R. Garey and D. S. Johnson, Computers and Intractability: The Guide to the Theory of NP-Completeness (Freeman, San Francisco, 1979; Mir, Moscow 1982.
4. C. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity (Prentice-Hall, Englewood Cliffs, 1982; Mir, Moscow, 1985).
5. H. Kellerer and U. Pferschy, "A New Fully Polynomial Approximation Scheme for the Knapsack Problem," J. Combinatorial Optimiz. 3, 59-71 (1999).
6. B. Korte, "Kombinatorische Optimierung und Algorithmische Prinzipien," in Ökonomische Prognose-, Entscheidungs-und Gleichgewichtsmodelle, Ed. by W. L. Krelle (VCH Verlagsgessellschaft, Weinheim, 1986), pp. 286-341.
7. B. Korte and J. Vygen, Combinatorial Optimization. Theory and Algorithms. 3rd Ed (Springer, Berlin, 2006).
8. K. Szkatula and M. Libura, "Probabilistic Analysis of Simple Algorithms for Binary Knapsack Problem," Control and Cybernetics 12, 147-157 (1983).
9. G. S. Lueker, "On the Average Difference between the Solutions to Linear and Integer Knapsack Problems," in Applied Probability-Computer Science, the Interface (Birkhauser, Basel, 1982), Vol. 1, pp. 489-504.
10. J. M. Calvin and J. Y. Leung, "Average-Case Analysis of a Greedy Algorithm for the 0/1 Knapsack Problem," Oper. Res. Letters 31, 202-210 (2003).
11. K-H. Borgwardt and B. Tremel, "The Average Quality of Greedy Algorithms for the Subset-Sum-Maximization Problem," Methods and Models of Operations Research, 35, 113-149 (1991).
12. R. Kohli, R. Krishnamurti, and P. Mirchandani, "Average Performance of Greedy Algorithms for the Integer Knapsack Problem," Eur. J Oper. Res 154, 36-45 (2004).
13. G. N. Diubin and A. A. Korbut, "Greedy Algorithms for the Knapsack Problem: Behavior in the Average," Sib. Zh. Industr. Mat. 2(2(4) (1999).
14. G. N. Diubin, A. A. Korbut, and I. Kh. Sigal, "Behavior in the Average of Greedy Methods for the Knapsack Problem," in Economic-Mathematic Investigations: Mathematical Models and Information Technologies, III (Nauka, St. Petersburg, 2003), pp. 46-54 [in Russian].
15. G. Diubin and A. Korbut, "The Average Behaviour of Greedy Algorithms for the Knapsack Problem: General Distributions," Math. Meth. Oper. Res 57(3), 449-479 (2003).
16. M. M. Guntzer and D. Jungnickel, "Approximate Minimization Algorithms for the 0/1 Knapsack and Subset-Sum Problem," Oper. Res. Lett 26, 55-66 (2000).
17. L. G. Babat, "Linear Functions on an N-dimensional Unit Cube," Dokl. Akad. Nauk SSSR 221(4), 761-762 (1975).
18. G. V. Gens and E. V. Levner, "Computational Complexity of Approximation Algorithms for Combinatorial Problems," in Mathematical Foundations of Computer Science (Lecture Notes in Computer Sciences, V. 74) (Springer, Berlin, 1979), pp. 292-300.
19. A. A. Korbut, "Characterization of Dual Greedy Algorithms on Independence Systems," in Economic-Mathematic Investigations: Mathematical Models and Information Technologies (Nauka, St. Petersburg, 2000), pp. 42-51 [in Russian].
20. I. Kh. Sigal and A. P. Ivanova, Introduction to Applied Discrete Programming (Fizmatlit, Moscow, 2002) [in Russian].