FASTSP: Linear time calculation of alignment accuracy

Motivation: 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. Results: In this article, we prove that each of these scores can be computed in linear time, and we present FastSP, a linear-time algorithm for calculating these scores. Even on the largest alignments we explored (one with 50 000 sequences), FastSP completed <2 min and used at most 2 GB of the main memory. The best alternative is qscore, a method whose empirical running time is approximately the same as FastSP when given sufficient memory (at least 8 GB), but whose asymptotic running time has never been theoretically established. In addition, for comparisons of large alignments under lower memory conditions (at most 4 GB of main memory), qscore uses substantial memory (up to 10 GB for the datasets we studied), took more time and failed to analyze the largest datasets.