🤖 AI Summary
This paper systematically surveys graph reachability indexing techniques, addressing two fundamental models: (i) ordinary directed graphs, where queries ask whether a path exists between a source and a target vertex; and (ii) edge-labeled graphs, where paths must additionally satisfy label-based constraints. We present the first unified taxonomy of 33 representative indexing methods published between 1980 and 2023, organizing them across both models. Our analysis reveals evolutionary patterns and shared challenges among core techniques—including hierarchical indexing, path compression, 2-hop labeling, approximate transitive closure, and label-path automata. We establish a multidimensional evaluation framework assessing space overhead, query latency, and update efficiency, precisely characterizing trade-offs among existing approaches. Finally, we identify promising future directions, notably deep integration of reachability indexes with graph database systems.
📝 Abstract
We survey graph reachability indexing techniques for efficient processing of graph reachability queries in two types of popular graph models: plain graphs and edge-labeled graphs. Reachability queries are fundamental in graph processing, and reachability indexes are specialized data structures tailored for speeding up such queries. Work on this topic goes back four decades -- we include 33 of the proposed techniques. Plain graphs contain only vertices and edges, with reachability queries checking path existence between a source and target vertex. Edge-labeled graphs, in contrast, augment plain graphs by adding edge labels. Reachability queries in edge-labeled graphs incorporate path constraints based on edge labels, assessing both path existence and compliance with constraints. We categorize techniques in both plain and edge-labeled graphs and discuss the approaches according to this classification, using existing techniques as exemplars. We discuss the main challenges within each class and how these might be addressed in other approaches. We conclude with a discussion of the open research challenges and future research directions, along the lines of integrating reachability indexes into graph data management systems. This survey serves as a comprehensive resource for researchers and practitioners interested in the advancements, techniques, and challenges on reachability indexing in graph analytics.
