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Given $n$ positive integers $a_1,a_2,\dots,a_n$, and a positive integer righthand side $\beta$, we consider the feasibility version of the subset sumproblem which is the problem of determining whether a subset of$a_1,a_2,\dots,a_n$ adds up to $\beta$. We show that if the right hand side$\beta$ is chosen as $\lfloor r\sum_{j=1}^n a_j \rfloor$ for a constant $0 < r< 1$ and if the $a_j$'s are independentand identically distributed from adiscrete uniform distribution taking values ${1,2,\dots,\lfloor 10^{n/2}\rfloor }$, then the probability that the instance of the subset sum problemgenerated requires the creation of an exponential number of branch-and-boundnodes when one branches on the individual variables in any order goes to $1$ as$n$ goes to infinity.

On the Hardness of Almost All Subset Sum Problems by Ordinary Branch-and-Bound