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Upper bound on the number of steps for solving the subset sum problem by the Branch-and-Bound method
We study the computational complexity of one of the particular cases of the
knapsack problem: the subset sum problem. For solving this problem we consider
one of the basic variants of the Branch-and-Bound method in which any
sub-problem is decomposed along the free variable with the maximal weight. By
the complexity of solving a problem by the Branch-and-Bound method we mean the
number of steps required for solving the problem by this method. In the paper
we obtain upper bounds on the complexity of solving the subset sum problem by
the Branch-and-Bound method. These bounds can be easily computed from the input
data of the problem. So these bounds can be used for the the preliminary
estimation of the computational resources required for solving the subset sum
problem by the Branch-and-Bound method