An Efficient Algorithm for Statistical Multiple Alignment on Arbitrary Phylogenetic Trees

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Abstract
We present an efficient algorithm for statistical multiple alignment based on the TKF91 model of Thorne, Kishino, and Felsenstein (1991) on an arbitrary k-leaved phylogenetic tree. The existing algorithms use a hidden Markov model approach, which requires at least O(√5k) states and leads to a time complexity of O(5kLk) , where L is the geometric mean sequence length. Using a combinatorial technique reminiscent of inclusion/exclusion, we are able to sum away the states, thus improving the time complexity to O(2kLk) and considerably reducing memory requirements. This makes statistical multiple alignment under the TKF91 model a definite practical possibility in the case of a phylogenetic tree with a modest number of leaves.