Theoretically and Practically Efficient Parallel Nucleus Decomposition

Summary: A work-optimal, low-depth parallel nucleus decomposition via a new clique-peeling bound, scalable clique listing/bucketing, and cache-efficient multi-level hashing. Practical optimizations deliver up to 55× speedup and enable million-scale decompositions. (summarized by gpt-5.6-luna on Jul 24 2026)

Paper ID: 13120
Venue: VLDB
Year: 2022
Pagerank: 5.8975125e-05
Overall Rank: 6,368 | 56.32%
DOI: 10.14778/3494124.3494140

Incoming Non-self Citations Over Time

Authors

1. Jessica Shi (Massachusetts Institute of Technology)
2. Laxman Dhulipala (Massachusetts Institute of Technology)
3. Julian Shun (Massachusetts Institute of Technology)

BibTeX Citation

@article{shi_vldb22,
        title = {{Theoretically and Practically Efficient Parallel Nucleus Decomposition}},
        author = {Shi, Jessica and Dhulipala, Laxman and Shun, Julian},
        journal = {PVLDB},
        series = {{VLDB} '22},
        volume = {15},
        number = {3},
        pages = {583--596},
        doi = {10.14778/3494124.3494140},
        url = {https://doi.org/10.14778/3494124.3494140},
        year = {2022}
}

Incoming Citations (Sorted by Pagerank)

Showing 5 of 5 citing papers.

Rank	Citing Paper	Year	Venue	Pagerank
6,617	Efficient Parallel D-core Decomposition at Scale	2024	VLDB	5.8212982e-05
9,695	Parallel Algorithms for Hierarchical Nucleus Decomposition	2024	SIGMOD	5.2351259e-05
10,273	Nucleus Decomposition Revisited: An Efficient Counting-Based Approach	2026	SIGMOD	5.093636e-05
10,772	Parallel k-Core Decomposition: Theory and Practice	2025	SIGMOD	5.093636e-05
11,256	Efficient Algorithms for Density Decomposition on Large Static and Dynamic Graphs	2024	VLDB	5.093636e-05

Outgoing Citations (Sorted by Pagerank)

Showing 18 of 18 cited papers.

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

Rank	Cited Paper	Year	Venue	Pagerank
102	Truss Decomposition in Massive Networks	2012	VLDB	0.00034255289
138	Discovering Large Dense Subgraphs in Massive Graphs	2005	VLDB	0.00029823423
189	Querying K-Truss Community in Large and Dynamic Graphs	2014	SIGMOD	0.00026114928
590	Large Scale Cohesive Subgraphs Discovery for Social Network Visual Analysis	2013	VLDB	0.0001605572
825	K-Core Decomposition of Large Networks on a Single PC	2016	VLDB	0.00013779895
1,018	Dense Subgraph Maintenance under Streaming Edge Weight Updates for Real-time Story Identification	2012	VLDB	0.0001263063
1,069	Truss-based Community Search: a Truss-equivalence Based Indexing Approach	2017	VLDB	0.00012323497
1,113	Approximate Closest Community Search in Networks	2016	VLDB	0.00012124571
1,416	Local Algorithms for Hierarchical Dense Subgraph Discovery	2019	VLDB	0.00010839488
2,024	Efficient Algorithms for Densest Subgraph Discovery	2019	VLDB	9.2907829e-05
2,083	Fast Hierarchy Construction for Dense Subgraphs	2017	VLDB	9.1976617e-05
2,243	Unboundedness and Efficiency of Truss Maintenance in Evolving Graphs	2019	SIGMOD	8.8813183e-05
2,826	Hierarchical Core Maintenance on Large Dynamic Graphs	2021	VLDB	8.0865974e-05
3,503	Accelerating Truss Decomposition on Heterogeneous Processors	2020	VLDB	7.3592701e-05
3,616	Parallel Local Graph Clustering	2016	VLDB	7.2559471e-05
5,294	Theoretically-Efficient and Practical Parallel DBSCAN	2020	SIGMOD	6.2790627e-05
7,624	RECEIPT: REfine CoarsE-grained IndePendent Tasks for Parallel Tip decomposition of Bipartite Graphs	2021	VLDB	5.5805027e-05
10,011	Sage: Parallel Semi-Asymmetric Graph Algorithms for NVRAMs	2020	VLDB	5.1772034e-05

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#	Overall Rank	Paper	Year	Venue
1	9,301	Accelerating Core Decomposition in Billion-Scale Hypergraphs	2025	SIGMOD
2	1,640	Distance-generalized Core Decomposition	2019	SIGMOD
3	10,100	Parallel Colorful h-star Core Maintenance in Dynamic Graphs	2023	VLDB
4	2,083	Fast Hierarchy Construction for Dense Subgraphs	2017	VLDB
5	1,416	Local Algorithms for Hierarchical Dense Subgraph Discovery	2019	VLDB
6	5,697	Local Algorithms for Distance-generalized Core Decomposition over Large Dynamic Graphs	2021	VLDB
7	6,617	Efficient Parallel D-core Decomposition at Scale	2024	VLDB
8	10,772	Parallel k-Core Decomposition: Theory and Practice	2025	SIGMOD
9	10,273	Nucleus Decomposition Revisited: An Efficient Counting-Based Approach	2026	SIGMOD
10	9,695	Parallel Algorithms for Hierarchical Nucleus Decomposition	2024	SIGMOD