Even Faster Geosocial Reachability Queries

TL;DR

This paper introduces 2DReach, a simplified and faster method for geosocial reachability queries that improves index construction speed and reduces storage while maintaining or enhancing query performance.

Contribution

The paper presents 2DReach, a novel approach that eliminates interval labelling, simplifies index structure, and offers compressed variants for efficient geosocial reachability querying.

Findings

2DReach has faster index construction than 3DReach.

Compressed variants reduce storage size significantly.

2DReach achieves comparable or better query performance.

Abstract

Geosocial reachability queries (\textsc{RangeReach}) determine whether a given vertex in a geosocial network can reach any spatial vertex within a query region. The state-of-the-art 3DReach method answers such queries by encoding graph reachability through interval labelling and indexing spatial vertices in a 3D R-tree. We present 2DReach, a simpler approach that avoids interval labelling entirely. Like 3DReach, 2DReach collapses strongly connected components (SCCs) into a DAG, but instead of computing interval labels, it directly stores a 2D R-tree per component over all reachable spatial vertices. A query then reduces to a single 2D R-tree lookup. We further propose compressed variants that reduce storage by excluding spatial sinks and sharing R-trees between components with identical reachable sets. Experiments on four real-world datasets show that 2DReach achieves faster index construction than 3DReach, with the compressed variant yielding the smallest index size among all methods. 2DReach delivers competitive or superior query performance with more stable response times across varying query parameters.