Compact Answers to Temporal Path Queries

TL;DR

This paper explores efficient methods for representing and querying temporal path data in graphs, focusing on compact encodings of time-based relations to improve storage and computation in dynamic network analysis.

Contribution

It introduces four novel compact representations for answers to temporal path queries, analyzing their advantages and limitations, including a refined encoding for dense time scenarios.

Findings

Most refined encoding allows finite representation over dense time.

Trade-offs identified between conciseness and computational cost.

Different encodings suit various types of temporal network queries.

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.