Efficient implied alignment

Alex J Washburn,Ward C Wheeler

doi:10.1186/s12859-020-03595-2

Abstract

BackgroundGiven a binary tree 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 mathcal {T}. This is done by first decorating each node of 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.ResultsPrevious descriptions of the implied alignment algorithm suggest a technique of “back-propagation” with time complexity mathcal {O}left (k^{2} * n^{2}right). Here we describe an implied alignment algorithm with complexity 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).ConclusionsThe reduction in the time complexity of the algorithm dramatically improves both its utility in generating multiple sequence alignments and its heuristic utility.

Highlights

Given a binary tree 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
Originally designed for alignmentfree phylogenetic analysis, the procedure was first used as a stand-alone multiple sequence alignment (MSA) tool by [11] in their analysis of skink systematics
The use of Implied Alignment (IA) as an MSA algorithm as well as its use in the “static approximation” procedure [22] benefits greatly from improvements in the time complexity we present in this paper

Summary

Introduction

Given a binary tree 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. This is done by first decorating each node of T with an alignment context using ⊗, in a post-order traversal, during a subsequent pre-order traversal, inferring on which edges insertion and deletion events occurred using those internal node decorations. Whiting et al found that IA was superior (in terms of tree optimality score) to other

Methods

Results

Discussion

Conclusion