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A Recursive Approach To The Implementation Of Enumerative Methods

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  • Lenstra, J. K.
  • Rinnooy Kan, A. H. G.

Abstract

Algorithms for generating permutations by means of both lexicographic and minimum-change methods are presented. A recursive approach to their implementation leads to transparent procedures that are easily proved correct; moreover, they turn out to be no less efficient than previous iterative generators. Some applications of explicit enumeration to combinatorial optimization problems, exploiting the minimum-change property, are indicated. Finally, a recursive approach to implicit enumeration is discussed.

Suggested Citation

  • Lenstra, J. K. & Rinnooy Kan, A. H. G., 1980. "A Recursive Approach To The Implementation Of Enumerative Methods," Econometric Institute Archives 272202, Erasmus University Rotterdam.
    • Handle: RePEc:ags:eureia:272202
    DOI: 10.22004/ag.econ.272202
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    References listed on IDEAS

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    1. J. K. Lenstra & A. H. G. Rinnooy Kan, 1978. "Technical Note—On the Expected Performance of Branch-and-Bound Algorithms," Operations Research, INFORMS, vol. 26(2), pages 347-349, April.
    2. Norman Agin, 1966. "Optimum Seeking with Branch and Bound," Management Science, INFORMS, vol. 13(4), pages 176-185, December.
    3. Vorst, A. C. F., 1980. "The General Linear Group Of Polynomial Rings Over Regular Rings," Econometric Institute Archives 272201, Erasmus University Rotterdam.
    4. Boender, C. G. E. & Rinnooy Kan, A. H. G. & Stougie, L. & Timmer, G. T., 1980. "A Stochastic Method For Global Optimization," Econometric Institute Archives 272200, Erasmus University Rotterdam.
    5. A. H. G. Rinnooy Kan & B. J. Lageweg & J. K. Lenstra, 1975. "Minimizing Total Costs in One-Machine Scheduling," Operations Research, INFORMS, vol. 23(5), pages 908-927, October.
    6. L. G. Mitten, 1970. "Branch-and-Bound Methods: General Formulation and Properties," Operations Research, INFORMS, vol. 18(1), pages 24-34, February.
    7. Egon Balas, 1968. "Letter to the Editor—A Note on the Branch-and-Bound Principle," Operations Research, INFORMS, vol. 16(2), pages 442-445, April.
    8. E. L. Lawler & D. E. Wood, 1966. "Branch-and-Bound Methods: A Survey," Operations Research, INFORMS, vol. 14(4), pages 699-719, August.
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    Cited by:

    1. Telgen, J., 1980. "The Complexity Of The Constrained Gradient Method For Linear Programming," Econometric Institute Archives 272204, Erasmus University Rotterdam.

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