Efficient Temporal Simple Path Graph Generation

2025-07-14

AI Summary

This paper addresses the problem of efficiently generating a temporal simple path subgraph (tspG) between a source and a target vertex over a given time interval, avoiding the exponential cost of explicitly enumerating all temporal simple paths. To this end, we formally define the tspG generation problem and propose a two-stage polynomial-time method: first, construct a compact upper-bound graph by jointly pruning with temporal and acyclicity constraints; second, precisely eliminate non-path edges via escape-edge verification. Our approach yields an approximate yet exact tspG—i.e., it guarantees correctness of the final output while achieving efficiency. Experiments on ten real-world temporal graphs demonstrate that our method achieves over two orders-of-magnitude speedup compared to brute-force enumeration, significantly improving scalability and practicality for large-scale temporal graph analysis.

Technology Category

• Planning, Routing, and Scheduling: Temporal Planning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Interactions between two entities often occur at specific timestamps, which can be modeled as a temporal graph. Exploring the relationships between vertices based on temporal paths is one of the fundamental tasks. In this paper, we conduct the first research to propose and investigate the problem of generating the temporal simple path graph (tspG), which is the subgraph consisting of all temporal simple paths from the source vertex to the target vertex within the given time interval. Directly enumerating all temporal simple paths and constructing the tspG is computationally expensive. To accelerate the processing, we propose an efficient method named Verification in Upper-bound Graph. It first incorporates the temporal path constraint and simple path constraint to exclude unpromising edges from the original graph, which obtains a tight upper-bound graph as a high-quality approximation of the tspG in polynomial time. Then, an Escape Edges Verification algorithm is further applied in the upper-bound graph to construct the exact tspG without exhaustively enumerating all temporal simple paths between given vertices. Finally, comprehensive experiments on 10 real-world graphs are conducted to demonstrate the efficiency and effectiveness of the proposed techniques.

Problem

• Generating temporal simple path graphs efficiently
• Reducing computational cost in path enumeration
• Verifying edges in upper-bound approximation graphs

Innovation

• Verification in Upper-bound Graph method
• Excludes unpromising edges efficiently
• Escape Edges Verification algorithm