Multivariate time series alignment is critical for ensuring coherent analysis across variables, but missing values and timestamp inconsistencies make this task highly challenging. Existing approaches often rely on prior imputation, which can introduce errors and lead to suboptimal alignments. To address these limitations, we propose a constraint-based alignment framework for incomplete multivariate time series that avoids imputation and ensures temporal and structural consistency. We further design efficient approximation algorithms to balance accuracy and scalability. Experiments on multiple real-world datasets demonstrate that our approach achieves superior alignment quality compared to existing methods under varying missing rates. Our contributions include: (1) formally defining incomplete multiple temporal data alignment problem; (2) proposing three approximation algorithms balancing accuracy and efficiency; and (3) validating our approach on diverse real-world datasets, where it consistently outperforms existing methods in alignment accuracy and the number of aligned tuples.

翻译：多变量时间序列对齐对于确保跨变量分析的连贯性至关重要，但缺失值和时间戳不一致性使得该任务极具挑战性。现有方法通常依赖先验插补，这可能引入误差并导致次优对齐。为应对这些局限，我们提出一种基于约束的不完整多变量时间序列对齐框架，该框架避免插补操作并确保时间与结构一致性。我们进一步设计了高效的近似算法以平衡精度与可扩展性。在多个真实数据集上的实验表明，在不同缺失率条件下，我们的方法相比现有方法实现了更优的对齐质量。我们的贡献包括：（1）形式化定义不完整多时序数据对齐问题；（2）提出三种平衡精度与效率的近似算法；（3）在多样化真实数据集上验证我们的方法，其在对齐精度和对齐元组数量方面均持续优于现有方法。