Abstract
We study the dynamic programming method. This method is one of the most general methods in a number of cases producing polynomial-time algorithms for solving discrete optimization problems. It is known that it runs in exponential time in the worst case. In this paper we show that under some conditions on the distribution of the input data of the multidimensional knapsack problem the dynamic programming method yields an algorithm for solving this problem which is polynomial in the average case. We also show that there is no approximation algorithm for solving the linear programming problem with Boolean variables whose performance ratio is essentially less than the trivial one (if P ≠ NP).
This research was partially supported by the Russian Foundation for Fundamental Research (Grant 93–01–01806).
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© 1996 Kluwer Academic Publishers
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Kuzyurin, N.N. (1996). An Integer Linear Programming Algorithm Polynomial in the Average Case. In: Korshunov, A.D. (eds) Discrete Analysis and Operations Research. Mathematics and Its Applications, vol 355. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1606-7_11
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DOI: https://doi.org/10.1007/978-94-009-1606-7_11
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