The auxiliary assignment problem is solved separately for each element for a given number of coordination spheres n spheres in order to obtain an initial guess for the non-linear assignment problem [Eq. (5)]. However, we need to take all solutions into account that yield the minimum number of formed and broken bonds within the auxiliary representation by extracting sets {S p } of indistinguishable atoms. In this context, indistinguishability of atoms refers to N being invariant under permutation of those atoms. The number n guess of initial guesses which we could construct by considering every combination of permutations from these sets quickly exceeds a manageable amount. Therefore, only a selection of n S sets is used to construct initial guesses such that a critical number τ guess is not exceeded: