Temporal graph patterns by timed automata

TL;DR

This paper introduces a novel approach using timed automata to express and evaluate complex temporal graph patterns, enabling more flexible and efficient detection of motifs in evolving graphs.

Contribution

It proposes a general framework for temporal graph pattern matching with timed automata and develops algorithms for efficient retrieval and evaluation of matches.

Findings

On-demand incremental algorithm excels with cyclic patterns on sparse graphs.

Maintaining partial matchings improves performance on acyclic or dense graphs.

Experimental results reveal trade-offs between different evaluation strategies.

Abstract

Temporal graphs represent graph evolution over time, and have been receiving considerable research attention. Work on expressing temporal graph patterns or discovering temporal motifs typically assumes relatively simple temporal constraints, such as journeys or, more generally, existential constraints, possibly with finite delays. In this paper we propose to use timed automata to express temporal constraints, leading to a general and powerful notion of temporal basic graph pattern (BGP). The new difficulty is the evaluation of the temporal constraint on a large set of matchings. An important benefit of timed automata is that they support an iterative state assignment, which can be useful for early detection of matches and pruning of non-matches. We introduce algorithms to retrieve all instances of a temporal BGP match in a graph, and present results of an extensive experimental evaluation, demonstrating interesting performance trade-offs. We show that an on-demand algorithm that processes total matchings incrementally over time is preferable when dealing with cyclic patterns on sparse graphs. On acyclic patterns or dense graphs, and when connectivity of partial matchings can be guaranteed, the best performance is achieved by maintaining partial matchings over time and allowing automaton evaluation to be fully incremental.