Challenges in Solving Sequence-to-Graph Alignment with Co-Linear Structure
Xingfu Li
TL;DR
The paper investigates two co-linear chaining formulations for sequence-to-graph alignment: Gap-CLC and Edit-CLC. It formalizes anchors via Cartesian-product occurrences in query sequences and pan-genome graphs, and defines the corresponding optimization objectives, including single-variant forms. Through linear-time reductions, it shows Gap-CLC inherits the hardness of exact seed matching under the Strong Exponential Time Hypothesis ($SETH$), ruling out sub-quadratic algorithms, while Edit-CLC is NP-hard when the graph contains errors. These results suggest that incorporating co-linear structure does not alleviate computational complexity, underscoring a need for practical algorithms and precise anchor representations to bridge theory and practice.
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 (SETH) 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 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.