Parametric k-best alignment

TL;DR

This paper introduces parametric k-best alignment, extending traditional parametric alignment to identify top k alignment summaries and their scoring regions, with polynomial complexity enabling genome-scale applications.

Contribution

It extends parametric alignment to k-best alignments, demonstrating polynomial complexity and enabling large-scale genomic analysis.

Findings

Complexity of parametric k-best alignment is polynomial in k.

Method is scalable to whole-genome sequences.

Enables analysis of suboptimal but biologically relevant alignments.

Abstract

Optimal sequence alignments depend heavily on alignment scoring parameters. Given input sequences, {\em parametric alignment} is the well-studied problem that asks for all possible optimal alignment summaries as parameters vary, as well as the {\em optimality region} of alignment scoring parameters which yield each optimal alignment. But biologically correct alignments might be {\em suboptimal} for all parameter choices. Thus we extend parametric alignment to {\em parametric $k$-best alignment}, which asks for all possible $k$-tuples of $k$-best alignment summaries $(s_1, s_2, ..., s_k)$, as well as the {\em $k$-best optimality region} of scoring parameters which make $s_1, s_2, ..., s_k$ the top $k$ summaries. By exploiting the integer-structure of alignment summaries, we show that, astonishingly, the complexity of parametric $k$-best alignment is only polynomial in $k$. Thus parametric $k$-best alignment is tractable, and can be applied at the whole-genome scale like parametric alignment.