Estimating the computational complexity of one variant of parallel realization of the branch-and-bound method for the knapsack problem

One of the possible realizations of the branch-and-bound method on multiprocessor systems with distributed memory, the front-end algorithm is addressed. The complexity of the front-end algorithm is studied for a family of Boolean knapsack problems with one constraint under the assumption that the number of processors is not limited. Formulas for the order of complexity growth with an increase in dimension of the problems from the addressed family are obtained for the front-end algorithm. The asymptotic acceleration behavior and efficiency of resource use with an increase in the number of variables are studied.