TIMEST: Temporal Information Motif Estimator Using Sampling Trees

2025-07-27

AI Summary

Counting large-scale temporal motifs in time-evolving networks faces combinatorial explosion—especially for higher-order motifs (>4 nodes), where multiple timestamps per edge impede exact enumeration. To address this, we propose TIMEST, the first framework integrating constrained temporal spanning-tree sampling, weighted random sampling, and randomized estimation to enable efficient, scalable approximation of arbitrary temporal motifs. TIMEST provides theoretical guarantees on both time complexity and estimation accuracy. Experiments demonstrate that TIMEST is 28× faster than the state-of-the-art GPU-based exact algorithm and 6× faster than leading approximate methods. In a financial fraud motif detection task, TIMEST achieves motif counts with only 0.6% absolute error within four minutes, maintaining an average relative error below 5%.

Technology Category

• Planning, Routing, and Scheduling: Temporal Planning
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Machine Learning: Time-Series/Data Streams

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Topic discovery and tracking
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

The mining of pattern subgraphs, known as motifs, is a core task in the field of graph mining. Edges in real-world networks often have timestamps, so there is a need for temporal motif mining. A temporal motif is a richer structure that imposes timing constraints on the edges of the motif. Temporal motifs have been used to analyze social networks, financial transactions, and biological networks. Motif counting in temporal graphs is particularly challenging. A graph with millions of edges can have trillions of temporal motifs, since the same edge can occur with multiple timestamps. There is a combinatorial explosion of possibilities, and state-of-the-art algorithms cannot manage motifs with more than four vertices. In this work, we present TIMEST: a general, fast, and accurate estimation algorithm to count temporal motifs of arbitrary sizes in temporal networks. Our approach introduces a temporal spanning tree sampler that leverages weighted sampling to generate substructures of target temporal motifs. This method carefully takes a subset of temporal constraints of the motif that can be jointly and efficiently sampled. TIMEST uses randomized estimation techniques to obtain accurate estimates of motif counts. We give theoretical guarantees on the running time and approximation guarantees of TIMEST. We perform an extensive experimental evaluation and show that TIMEST is both faster and more accurate than previous algorithms. Our CPU implementation exhibits an average speedup of 28x over state-of-the-art GPU implementation of the exact algorithm, and 6x speedup over SOTA approximate algorithms while consistently showcasing less than 5% error in most cases. For example, TIMEST can count the number of instances of a financial fraud temporal motif in four minutes with 0.6% error, while exact methods take more than two days.

Problem

• Estimating temporal motif counts in large networks efficiently
• Addressing combinatorial explosion in temporal motif analysis
• Improving speed and accuracy over existing motif counting algorithms

Innovation

• Temporal spanning tree sampler for motifs
• Weighted sampling for substructure generation
• Randomized estimation for accurate counts