Methods, computer-readable media, and apparatuses are disclosed for reconciling sets of financial transactions. A reconciliation input set of positive and negative numbers may be received, and a positive subset size and negative subset size may be determined for one or more reconciliation attempts. Maximum and minimum subset sums for the positive and negative subset sizes may be determined, and certain overlapping and non-overlapping portions may be identified between the positive subset sum range and the negative subset sum range. For any overlapping portions, a plurality of subset sum comparisons may be performed between positive subsets of the determined positive subset size and negative subsets of the determined negative subset size.