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An algorithm for the solution of the 0-1 knapsack problem. (English) Zbl 0468.90045

MSC:
90C09 Boolean programming
90C08 Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)
65K05 Numerical mathematical programming methods
68Q25 Analysis of algorithms and problem complexity
90-04 Software, source code, etc. for problems pertaining to operations research and mathematical programming
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[1] Balas, E., Zemel, E.: An algorithm for large zero-one knapsack problems. Operations Research28, 1130–1154 (1980). · Zbl 0449.90064
[2] Fayard, D., Plateau, G.: Resolution of the 0–1 knapsack problem: comparison of methods. Mathematical Programming8, 272–307 (1975). · Zbl 0314.90062
[3] Fayard, D., Plateau, G.: Techniques de résolution du problème du knapsack en variables bivalentes: partie III. Publication 91, Laboratoire de Calcul, Université des Sciences et Techniques de Lille I, France (1977).
[4] Fayard, D., Plateau, G.: Reduction algorithms for single and multiple constraints 0–1 linear programming problems. Proceedings of the Congress Methods of Mathematical Programming, Zakopane, Poland, 1977.
[5] Fayard, D., Plateau, G.: On ”an efficient algorithm for the 0–1 knapsack problem, by Robert M. Nauss”. Management Science24, 918–919 (1978). · Zbl 0483.68063
[6] Fayard, D., Plateau, G.: Contribution à la résolution des programmes mathématiques en nombres entiers, Thèse d’Etat, Université des Sciences et Techniques de Lille I France, 1979.
[7] Greenberg, H., Hegerich, R. L.: A branch search algorithm for the knapsack problem. Management Science16, 327–332 (1970). · Zbl 0191.48401
[8] Lawler, E. L.: Fast approximation algorithms for knapsack problems. Mathematics of Operations Research4, 339–356 (1979). · Zbl 0425.90064
[9] Martello, S., Toth, P.: Algorithm for the solution of the 0–1 single knapsack. Computing21, 81–86 (1978). · Zbl 0389.90070
[10] Sedgewick, R.: Implementing Quicksort programs. Communications of ACM21, 847–857 (1978). · Zbl 0386.68058
[11] Walukiewicz, S.: The size reduction of a binary knapsack problem. Bulletin of the Polish Academy of Sciences, Series Sciences and Technics23 (1975). · Zbl 0322.90040
[12] Zoltners, A. A.: A direct descent binary knapsack problem. Journal of ACM25, 304–311 (1978). · Zbl 0372.68012
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