Mathematics & AI

ISSN: 0000-0000 · EN

Mathematics & AI is an open-access, peer-reviewed journal at the intersection of mathematics and artificial intelligence. The journal publishes original research in mathematical foundations of AI, machine learning theory, optimization, statistical learning, neural network analysis, computational mat...

Hybrid Bi-Level Index for Shortest Paths in Temporal Networks

MathAI 2026 Selected Papers Special Issue
Published: May 21, 2026 Received: April 13, 2026

Abstract

Temporal graphs provide a natural model for dynamic relational data arising in modern AI systems, including event streams, temporal knowledge graphs, interaction networks, and transaction systems. Efficient reachability querying in such graphs constitutes a fundamental operation underlying temporal reasoning, feature extraction, and dynamic graph learning. In this paper, we propose a parameterized hybrid indexing framework for temporal reachability queries. Vertices are adaptively partitioned into two classes depending on the size of their reachable sets, enabling a controllable trade-off between memory usage and query time. Assuming a power-law degree distribution, we derive an analytical model for the proportion of promoted (large) vertices as a function of a promotion threshold. Closed-form asymptotic estimates for memory consumption and expected query time are obtained. We further prove the existence of a unique optimal threshold minimizing a combined memory–time cost functional. Theoretical predictions are validated experimentally, revealing a characteristic U-shaped dependence of query time on the promotion parameter. The results provide a mathematically grounded foundation for adaptive indexing in large-scale temporal graph analytics and AI-driven dynamic data systems.

Cite this article

Vasilev, M. Hybrid Bi-Level Index for Shortest Paths in Temporal Networks. Mathematics & AI 2026, 1, 11. https://enigma.ist/j/mathematics-ai/1/2/11

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