Efficient implied alignment

Abstract

Abstract Background Given a binary tree $\mathcal {T}$ T of n leaves, each leaf labeled by a string of length at most k, and a binary string alignment function ⊗, an implied alignment can be generated to describe the alignment of a dynamic homology for $\mathcal {T}$ T . This is done by first decorating each node of $\mathcal {T}$ T with an alignment context using ⊗, in a post-order traversal, then, during a subsequent pre-order traversal, inferring on which edges insertion and deletion events occurred using those internal node decorations. Results Previous descriptions of the implied alignment algorithm suggest a technique of “back-propagation” with time complexity $\mathcal {O}\left (k^{2} * n^{2}\right)$ O k 2 ∗ n 2 . Here we describe an implied alignment algorithm with complexity $\mathcal {O}\left (k * n^{2}\right)$ O k ∗ n 2 . For well-behaved data, such as molecular sequences, the runtime approaches the best-case complexity of Ω(k∗n). Conclusions The reduction in the time complexity of the algorithm dramatically improves both its utility in generating multiple sequence alignments and its heuristic utility.