A New Lower Bounding Paradigm and Tighter Lower Bounds for Elastic Similarity Measures

2026-03-16

AI Summary

Elastic similarity measures such as DTW, ERP, and MSM incur substantial computational overhead, necessitating efficient lower bounds to accelerate time series search. This work proposes a novel paradigm based on edge covering in bipartite graphs, unifying lower bound construction as a vertex-weighted optimization problem and introducing BGLB—a tighter lower bounding method. By incorporating enhancement terms, BGLB is theoretically guaranteed to strictly dominate existing lower bounds. Extensive experiments across 128 real-world datasets demonstrate that BGLB consistently provides the tightest lower bounds for six mainstream elastic measures, yielding speedups of 24.6%–84.9% in nearest neighbor search and significantly accelerating downstream tasks such as density-based clustering.

Technology Category

• Search and Optimization: Distributed Search
• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Data Compression

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Elastic similarity measures are fundamental to time series similarity search because of their ability to handle temporal misalignments. These measures are inherently computationally expensive, therefore necessitating the use of lower bounds to prune unnecessary comparisons. This paper proposes a new \emph{Bipartite Graph Edge-Cover Paradigm} for deriving lower bounds, which applies to a broad class of elastic similarity measures. This paradigm formulates lower bounding as a vertex-weighting problem on a weighted bipartite graph induced from the input time series. Under this paradigm, most of the existing lower bounds of elastic similarity measures can be viewed as simple instantiations. We further propose \textit{BGLB}, an instantiation of the proposed paradigm that incorporates an additional augmentation term, yielding lower bounds that are provably tighter. Theoretical analysis and extensive experiments on 128 real-world datasets demonstrate that \textit{BGLB} achieves the tightest known lower bounds for six elastic measures (ERP, MSM, TWED, LCSS, EDR, and SWALE). Moreover, \textit{BGLB} remains highly competitive for \textit{DTW} with a favorable trade-off between tightness and computational efficiency. In nearest neighbor search, integrating \textit{BGLB} into filter pipelines consistently outperforms state-of-the-art methods, achieving speedups ranging from $24.6\%$ to $84.9\%$ across various elastic similarity measures. Besides, \textit{BGLB} also delivers a significant acceleration in density-based clustering applications, validating the practical potential of \textit{BGLB} in time series similarity search tasks based on elastic similarity measures.

Problem

• elastic similarity measures
• lower bounds
• time series similarity search
• computational efficiency
• temporal misalignments

Innovation

• Bipartite Graph Edge-Cover Paradigm
• BGLB
• elastic similarity measures
• tighter lower bounds
• time series similarity search