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.

翻译：序列比对是计算生物学中评估生物序列间相似性与差异性的基石技术。其关键变体——序列-图比对——在有效捕捉遗传变异方面发挥着至关重要的作用。在本工作中，我们在此框架内引入了两种新颖的公式化问题：间隙敏感的共线性链式（Gap-CLC）问题以及基于编辑距离的含错误共线性链式（Edit-CLC）问题，并研究了它们的计算复杂性。我们证明，除非强指数时间假设（SETH）不成立，否则以亚二次时间解决Gap-CLC问题是极不可能的——即使在限制于二元字母表的情况下也是如此。此外，我们确立了当图中存在错误时，Edit-CLC问题是NP难的。这些发现强调，将共线性结构纳入序列-图比对模型并不能降低计算复杂性，这表明这些模型在计算上至少与缺乏此类先验信息的模型同样难以求解。