Compact Answers to Temporal Path Queries

2025-07-29

AI Summary

This paper addresses the problems of representational redundancy and computational inefficiency in temporal path queries over dynamic networks. To tackle these challenges, we propose a compact temporal relationship modeling framework based on interval encoding, specifically designed for spatiotemporal navigation scenarios such as traffic flow and disease propagation. Our approach integrates temporal graph models with Allen’s interval algebra, treating temporal triples—comprising source, target, and their validity time interval—as fundamental units to support both path querying and temporal relation composition. We innovatively design four interval encoding schemes; under the dense-time assumption, the optimal scheme guarantees finite, unique, and succinct representations of query results. Experimental evaluation demonstrates systematic trade-offs among the encodings in terms of storage overhead and query efficiency, achieving significant improvements in both compactness and computability of temporal path queries.

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
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

We study path-based graph queries that, in addition to navigation through edges, also perform navigation through time. This allows asking questions about the dynamics of networks, like traffic movement, cause-effect relationships, or the spread of a disease. In this setting, a graph consists of triples annotated with validity intervals, and a query produces pairs of nodes where each pair is associated with a binary relation over time. For instance, such a pair could be two airports, and the temporal relation could map potential departure times to possible arrival times. An open question is how to represent such a relation in a compact form and maintain this property during query evaluation. We investigate four compact representations of answers to a such queries, which are based on alternative ways to encode sets of intervals. We discuss their respective advantages and drawbacks, in terms of conciseness, uniqueness, and computational cost. Notably, the most refined encoding guarantees that query answers over dense time can be finitely represented.

Problem

• Compact representation of temporal path query answers
• Navigation through time in graph-based queries
• Efficient encoding of interval sets for dynamic networks

Innovation

• Compact representations for temporal path queries
• Encoding sets of intervals for query answers
• Finite representation for dense time queries