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The efficiency of an algorithm of integer programming: a probabilistic analysis


Author: Vladimir Lifschitz
Journal: Proc. Amer. Math. Soc. 79 (1980), 72-76
MSC: Primary 90C10; Secondary 68C25
DOI: https://doi.org/10.1090/S0002-9939-1980-0560587-2
MathSciNet review: 560587
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Abstract: A simple algorithm for solving the knapsack problem is shown to lead to examining, on the average, around $ {e^{2\sqrt n }}$ vectors out of $ {2^n}$.


References [Enhancements On Off] (What's this?)

  • [1] V. Klee and G. I. Minty, How good is the simplex algorithm?, Inequalities. III (Proc. Third Sympos., Univ. California, Los Angeles, Calif., 1969), Academic Press, New York, 1972, pp. 159-175. MR 0332165 (48:10492)
  • [2] R. Karp, Reducibility among combinatorial problems, Complexity of Computer Computations, R. E. Miller and J. W. Thatcher (Eds.), Plenum Press, New York, 1972, pp. 85-104. MR 0378476 (51:14644)
  • [3] E. Horowitz and S. Sahni, Computing partitions with application to the knapsack problem, J. Assoc. Comput. Mach. 21 (1974), 277-292. MR 0354006 (50:6488)
  • [4] D. Knuth, Estimating the efficiency of backtrack programs, Math. Comput. 29 (1975), 121-136. MR 0373371 (51:9571)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0560587-2
Keywords: Knapsack problem, algorithm analysis, average computing time
Article copyright: © Copyright 1980 American Mathematical Society

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