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GRAIL: Scalable Reachability Index for Large Graphs

Summary: GRAIL uses randomized interval labeling to build a scalable reachability index for massive directed graphs. Linear indexing time/space; query time ranges from constant to linear, enabling reachability on graphs with millions of nodes/edges where prior methods fail to scale. (summarized by gpt-5-nano on Feb 09 2026)

Paper ID
10084
Venue
VLDB
Year
2010
Pagerank
0.00017462279
Overall Rank
727 | 94.95%
DOI
-

Incoming Non-self Citations Over Time

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Incoming Citations (Sorted by Pagerank)

Showing 25 of 25 citing papers.

Rank Citing Paper Year Venue Pagerank
1,392 Real-time Constrained Cycle Detection in Large Dynamic Graphs 2018 VLDB 0.00012224015
1,448 Distance-Constraint Reachability Computation in Uncertain Graphs 2011 VLDB 0.00011928845
1,572 Query Preserving Graph Compression 2012 SIGMOD 0.00011296109
1,776 Reachability Queries on Large Dynamic Graphs: A Total Order Approach 2014 SIGMOD 0.0001058029
1,879 TF-Label: a Topological-Folding Labeling Scheme for Reachability Querying in a Large Graph 2013 SIGMOD 0.00010227906
2,762 K-Reach: Who is in Your Small World 2012 VLDB 8.1614818e-05
2,832 Regular Path Query Evaluation on Streaming Graphs 2020 SIGMOD 8.048358e-05
3,130 SCARAB: Scaling Reachability Computation on Large Graphs 2012 SIGMOD 7.5054361e-05
3,221 Landmark Indexing for Evaluation of Label-Constrained Reachability Queries 2017 SIGMOD 7.3541078e-05
3,234 Managing Large Dynamic Graphs Efficiently 2012 SIGMOD 7.3302974e-05
3,235 iBFS: Concurrent Breadth-First Search on GPUs 2016 SIGMOD 7.3298263e-05
3,676 Simple, Fast, and Scalable Reachability Oracle 2013 VLDB 6.8500097e-05
3,949 Efficient Reachability Query Evaluation in Large Spatiotemporal Contact Datasets 2012 VLDB 6.5929931e-05
4,478 Reachability Querying: An Independent Permutation Labeling Approach 2014 VLDB 6.1452192e-05
5,030 Making Graphs Compact by Lossless Contraction 2021 SIGMOD 5.7445683e-05
5,488 Microblog Entity Linking with Social Temporal Context 2015 SIGMOD 5.4798261e-05
5,548 Efficiently Answering Reachability and Path Queries on Temporal Bipartite Graphs 2021 VLDB 5.4445937e-05
6,531 Labeling Workflow Views with Fine-Grained Dependencies 2012 VLDB 5.0196961e-05
6,796 Answering Billion-Scale Label-Constrained Reachability Queries within Microsecond 2020 VLDB 4.9195203e-05
7,595 DAG Reduction: Fast Answering Reachability Queries 2017 SIGMOD 4.6980168e-05
7,714 Minimum Strongly Connected Subgraph Collection in Dynamic Graphs 2024 VLDB 4.6651585e-05
8,056 Labeling Recursive Workflow Executions On-the-Fly 2011 SIGMOD 4.5903524e-05
8,667 Distributed Set Reachability 2016 SIGMOD 4.467539e-05
9,897 Top-k Relevant Semantic Place Retrieval on Spatial RDF Data 2016 SIGMOD 4.2559233e-05
12,049 I/O Efficient: Computing SCCs in Massive Graphs 2013 SIGMOD 4.1905499e-05
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Outgoing Citations (Sorted by Pagerank)

Showing 4 of 4 cited papers.

Citations counted here include only citations to other VLDB/SIGMOD/CIDR/PODS papers in this database.

Rank Cited Paper Year Venue Pagerank
255 Efficient Management of Transitive Relationships in Large Data and Knowledge Bases 1989 SIGMOD 0.00030342925
280 3-HOP: A High-Compression Indexing Scheme for Reachability Query 2009 SIGMOD 0.00029092277
334 Fast and Practical Indexing and Querying of Very Large Graphs 2007 SIGMOD 0.00027077424
784 Efficiently Answering Reachability Queries on Very Large Directed Graphs 2008 SIGMOD 0.00016648392
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Semantically Similar Papers

Overall Rank Paper Year Venue Pagerank
2,958 Computing Label-Constraint Reachability in Graph Databases 2010 SIGMOD 7.8126329e-05
6,796 Answering Billion-Scale Label-Constrained Reachability Queries within Microsecond 2020 VLDB 4.9195203e-05
9,485 I/O Efficient Label-Constrained Reachability Queries in Large Graphs 2024 VLDB 4.3300131e-05
2,762 K-Reach: Who is in Your Small World 2012 VLDB 8.1614818e-05
3,676 Simple, Fast, and Scalable Reachability Oracle 2013 VLDB 6.8500097e-05
4,478 Reachability Querying: An Independent Permutation Labeling Approach 2014 VLDB 6.1452192e-05
784 Efficiently Answering Reachability Queries on Very Large Directed Graphs 2008 SIGMOD 0.00016648392
1,776 Reachability Queries on Large Dynamic Graphs: A Total Order Approach 2014 SIGMOD 0.0001058029
334 Fast and Practical Indexing and Querying of Very Large Graphs 2007 SIGMOD 0.00027077424
3,130 SCARAB: Scaling Reachability Computation on Large Graphs 2012 SIGMOD 7.5054361e-05