Complexity of Sequence-to-Graph Alignment with Co-Linear Chaining

TL;DR

This paper investigates the computational complexity of two new sequence-to-graph alignment problems, revealing they are computationally hard, thus challenging assumptions about simplifying such models with co-linear structures.

Contribution

The paper introduces two novel formulations of sequence-to-graph alignment problems and proves their computational hardness, showing that co-linear structures do not simplify the complexity.

Findings

Gap-CLC cannot be solved in sub-quadratic time unless SETH fails.

Edit-CLC is NP-hard with errors in pan-genome graphs.

Co-linear structures do not reduce the computational complexity of sequence-to-graph alignment.

Abstract

Sequence alignment is a cornerstone technique in computational biology for assessing similarities and differences among biological sequences. A key variant, sequence-to-graph alignment, plays a crucial role in effectively capturing genetic variations. In this work, we introduce two novel formulations within this framework: the Gap-sensitive Co-Linear Chaining (Gap-CLC) problem and the Co-Linear Chaining with Errors based on Edit Distance (Edit-CLC) problem, and we investigate their computational complexity. We show that solving the Gap-CLC problem in sub-quadratic time is highly unlikely unless the Strong Exponential Time Hypothesis fails -- even when restricted to binary alphabets. Furthermore, we establish that the Edit-CLC problem is NP-hard in the presence of errors within the pan-genome graph. These findings emphasize that incorporating co-linear structures into sequence-to-graph alignment models fails to reduce computational complexity, highlighting that these models remain at least as computationally challenging to solve as those lacking such prior information.