Hybrid Bi-Level Index for Shortest Paths in Temporal Networks

Vasilev M.

Keywords: temporal networks, shortest paths, dynamic graphs, memory–time trade-off, power-law graphs

TL;DR: A hybrid indexing method for shortest paths in temporal graphs with an analytically optimized promotion threshold

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.

Submission Number: 21