Multiple sequence alignment is a basic part of much biological research, including phylogeny estimation and protein structure and function prediction. Different alignments on the same set of unaligned sequences are often compared, sometimes in order to assess the accuracy of alignment methods or to infer a consensus alignment from a set of estimated alignments. Three of the standard techniques for comparing alignments, Developer, Modeler and Total Column (TC) scores can be derived through calculations of the set of homologies that the alignments share. However, the brute-force technique for calculating this set is quadratic in the input size. The remaining standard technique, Cline Shift Score, inherently requires quadratic time.