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Complexity of solving the Subset Sum problem with the branch-and-bound method with domination and cardinality filtering

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Abstract

We obtain an exact upper bound on the complexity of solving the Subset Sum problem with a variation of the branch-and-bound method of a special form. Complexity is defined as the number of subproblems considered in the process of solving the original problem. Here we reduce the enumeration by using the domination relation. We construct an instance of the Subset Sum problem on which our bound is realized. The resulting bound is asymptotically twice smaller than the exact upper bound on the complexity of solving this problem with a standard version of the branch-and-bound method.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    R. M. Kolpakov

  2. Dorodnicyn Computing Centre, Russian Academy of Sciences, Moscow, Russia

    R. M. Kolpakov & M. A. Posypkin

  3. Moscow Institute of Electronic Equipment, Moscow, Russia

    Si Tu Tant Sin

Authors
  1. R. M. Kolpakov
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  2. M. A. Posypkin
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  3. Si Tu Tant Sin
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Correspondence to R. M. Kolpakov.

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Original Russian Text © R.M. Kolpakov, M.A. Posypkin, Si Tu Tant Sin, 2017, published in Avtomatika i Telemekhanika, 2017, No. 3, pp. 96–110.

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Kolpakov, R.M., Posypkin, M.A. & Sin, S.T.T. Complexity of solving the Subset Sum problem with the branch-and-bound method with domination and cardinality filtering. Autom Remote Control 78, 463–474 (2017). https://doi.org/10.1134/S0005117917030079

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  • DOI: https://doi.org/10.1134/S0005117917030079

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