Generalized Hypertree Decompositions: NP-Hardness and Tractable Variants

Summary: Shows that deciding generalized hypertree width GHW(H) ≤ k is NP-hard already for k=3, and that the tree-projection existence problem is NP-complete, settling long-standing open problems. Proposes a framework where any tractable GHD-approximation is dominated by partial-edge functions and introduces Component Hypertree Decompositions as a tractable, strictly more general approximation. (summarized by gpt-5-mini on Feb 09 2026)

Paper ID: 1411
Venue: PODS
Year: 2007
Pagerank: 0.00018973823
Overall Rank: 626 | 95.65%
DOI: -

Incoming Non-self Citations Over Time

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Incoming Citations (Sorted by Pagerank)

Showing 20 of 20 citing papers.

Rank	Citing Paper	Year	Venue	Pagerank
502	Worst-case Optimal Join Algorithms	2012	PODS	0.00021526612
1,328	Hypertree Decompositions: Questions and Answers	2016	PODS	0.00012565612
1,557	Beyond Worst-case Analysis for Joins with Minesweeper	2014	PODS	0.00011392493
2,063	Counting Solutions to Conjunctive Queries: Structural and Hybrid Tractability	2014	PODS	9.6447857e-05
3,715	Optimal Algorithms for Ranked Enumeration of Answers to Full Conjunctive Queries	2020	VLDB	6.8220943e-05
4,058	Efficient Evaluation and Approximation of Well-designed Pattern Trees	2015	PODS	6.4866036e-05
5,053	DunceCap: Query Plans Using Generalized Hypertree Decompositions	2015	SIGMOD	5.7323846e-05
5,077	HyperBench: A Benchmark and Tool for Hypergraphs and Empirical Findings	2019	PODS	5.7153846e-05
5,855	Optimal Join Algorithms Meet Top-k	2020	SIGMOD	5.3006096e-05
6,949	Tree-Width and Functional Dependencies in Databases	2008	PODS	4.8898337e-05
7,162	Computing the Difference of Conjunctive Queries Efficiently	2023	SIGMOD	4.8132423e-05
7,467	Yannakakis+: Practical Acyclic Query Evaluation with Theoretical Guarantees	2025	SIGMOD	4.7218691e-05
7,473	The Power of Tree Projections: Local Consistency, Greedy Algorithms, and Larger Islands of Tractability	2010	PODS	4.7198203e-05
7,501	Ranked Enumeration of Minimal Triangulations	2019	PODS	4.7180617e-05
8,486	Fast Parallel Hypertree Decompositions in Logarithmic Recursion Depth	2022	PODS	4.4999394e-05
8,851	Efficient Approximations of Conjunctive Queries	2012	PODS	4.4363908e-05
9,031	Extending SQL to Return a Subdatabase	2025	SIGMOD	4.4039656e-05
9,091	Efficiently Enumerating Minimal Triangulations	2017	PODS	4.39823e-05
10,360	Soft and Constrained Hypertree Width	2025	PODS	4.1945683e-05
11,324	The Complexity of Conjunctive Queries with Degree 2	2022	PODS	4.1945683e-05

Outgoing Citations (Sorted by Pagerank)

Showing 2 of 2 cited papers.

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

Rank	Cited Paper	Year	Venue	Pagerank
1,038	Weighted Hypertree Decompositions and Optimal Query Plans	2004	PODS	0.00014492414
2,015	Robbers, Marshals, and Guards: Game Theoretic and Logical Characterizations of Hypertree Width	2001	PODS	9.7901938e-05

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10,360	Soft and Constrained Hypertree Width	2025	PODS	4.1945683e-05
7,473	The Power of Tree Projections: Local Consistency, Greedy Algorithms, and Larger Islands of Tractability	2010	PODS	4.7198203e-05
11,324	The Complexity of Conjunctive Queries with Degree 2	2022	PODS	4.1945683e-05
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10,483	Fast Hypertree Decompositions via Linear Programming: Fractional and Generalized	2025	SIGMOD	4.1945683e-05
1,328	Hypertree Decompositions: Questions and Answers	2016	PODS	0.00012565612
11,132	A Branch-&-Bound Algorithm for Fractional Hypertree Decomposition	2024	VLDB	4.1945683e-05
2,796	Hypertree Decompositions and Tractable Queries	1999	PODS	8.1112658e-05