Fast Fitch-parsimony algorithms for large data sets

The speed of analytical algorithms becomes increasingly important as systematists accumulate larger data sets. In this paper I discuss several time-saving modifications to published Fitch-parsimony tree search algorithms, including shortcuts that allow rapid evaluation of tree lengths and fast reoptimization of trees after clipping or joining of subtrees, as well as search strategies that allows one to successively increase the exhaustiveness of branch swapping. I also describe how Fitch-parsimony algorithms can be restructured to take full advantage of the computing power of modern microprocessors by horizontal or vertical packing of characters, allowing simultaneous processing of many characters, and by avoidance of conditional branches that disturb instruction flow. These new multicharacter algorithms are particularly useful for large data sets of characters with a small number of states, such as nucleotide characters. As an example, the multicharacter algorithms are estimated to be 3.6-10 times faster than single-character equivalents on a PowerPC 604. The speed gain is even larger on processors using MMX, Altivec or similar technologies allowing single instructions to be performed on multiple data simultaneously. (C) 1998 The Willi Hennig Society.