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Fast Fourier Transform and its applications to integer knapsack problems

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  • NESTEROV, Yu

Abstract

In this paper we suggest a new e.cient technique for solving integer knapsack problems. Our algorithms can be seen as application of Fast Fourier Transform to generating functions of integer polytopes.Using this approach, it is possible to count the number of boolean solutions of a single n-dimensional Diophantine equation {a, x} = b in O(//a//1 ln//a1//lnn) operations. Another application example is an integer knapsack optimization problem of volume b, which can be solved in O(//a//1 ln//a1//ln n + b lnsq.2n) operations of exact real arithmetics. These complexity estimates improve by a factor of n the complexity of the traditional Dynamic Programming technique.

Suggested Citation

  • NESTEROV, Yu, 2004. "Fast Fourier Transform and its applications to integer knapsack problems," LIDAM Discussion Papers CORE 2004064, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2004064
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2004.html
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    1. NESTEROV, Yu., 2003. "Characteristic functions of directed graphs and applications to stochastic equilibrium problems," LIDAM Discussion Papers CORE 2003013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Dimitris Bertsimas & Bradley Sturt, 2020. "Computation of Exact Bootstrap Confidence Intervals: Complexity and Deterministic Algorithms," Operations Research, INFORMS, vol. 68(3), pages 949-964, May.

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