One notable aspect of the EucDist algorithm involved checking for duplicate entries, which occasionally occurred in the simulated data from ACD labs. To differentiate these entries for the matching algorithm, a small fraction (1 -10 ) was added to them in cases where they needed to be assigned to two distinct peaks due to molecular symmetry breaking. Subsequently, the Euclidean distance between each pair of point s was computed and sorted by the shortest distance. The nearest points were then identified as a match and removed from the list to prevent double assignment. Any remaining points in the larger set were either matched with zeros or double-assigned by comparing them once again to the entire sequence of the smaller set, ensuring the most optimal double match.