Efficient implied alignment

Abstract

Abstract Background Given a binary tree T $\mathcal {T}$ 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 T $\mathcal {T}$ . This is done by first decorating each node of T $\mathcal {T}$ 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 O k 2 ∗ n 2 $\mathcal {O}\left (k^{2} * n^{2}\right)$ . Here we describe an implied alignment algorithm with complexity O k ∗ n 2 $\mathcal {O}\left (k * n^{2}\right)$ . 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.

Keywords

• Dynamic homology
• Implied alignment
• Multiple string alignment
• Phylogenetics
• Sequence alignment
• Tree alignment