Worst-Case Optimal BGPs on Temporal Graphs

2026-07-22

AI Summary

This work addresses the problem of efficiently evaluating extended basic graph pattern (BGP) queries over temporal graphs with edge-wise validity intervals, supporting quaternary queries involving temporal variables and ordering constraints, and returning all satisfying assignments of both variables and timestamps. To this end, it introduces worst-case optimal join techniques into temporal graph querying for the first time, proposing a novel index structure that supports arbitrary variable evaluation orders and requires only O(N) space. The approach adapts the Leapfrog Triejoin algorithm to achieve a worst-case optimal query complexity of O(Q·m log N). Experimental results demonstrate millisecond-level response times on real-world datasets, along with low memory overhead and high scalability.

Abstract

We study how to evaluate basic graph patterns (BGPs) in a worst-case-optimal (wco) manner over {\em temporal} labeled graphs, where edges have an interval of temporal validity. We adopt a flexible query language in which users specify m quads of the form (subject, property, object, time), using constants or variables. The time component denotes the instant at which a particular edge is valid, and users may also include order relations between temporal constants or variables. The answer is the set of all valid variable assignments, including time. We describe an index structure that, for a temporal graph with N edges, requires O(N) space and can evaluate extended BGPs in wco time O(Q* m log N), where Q* represents the maximum number of solutions for query Q over any temporal graph with the same number of instants of edge validity. We use our index to adapt Leapfrog Triejoin to the temporal graph setting under any variable evaluation ordering. Our index further yields wco guarantees for related query types, including snapshot evaluation, version queries, and other temporal variants. Experiments on real-world datasets show that our approach answers realistic queries in milliseconds with low space overhead.

Problem

• temporal graphs
• basic graph patterns
• worst-case optimal
• query evaluation
• time intervals

Innovation

• worst-case optimal
• temporal graphs
• basic graph patterns
• Leapfrog Triejoin
• time-aware indexing