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Simple Linear-Time Algorithms to Test Chordality of Graphs, Test Acyclicity of Hypergraphs, and Selectively Reduce Acyclic Hypergraphs
Abstract
Chordal graphs arise naturally in the study of Gaussian elimination on sparse symmetric matrices; acyclic hypergraphs arise in the study of relational data bases. Rose, Tarjan and Lueker [SIAM J. Comput., 5 (1976), pp. 266–283] have given a linear-time algorithm to test whether a graph is chordal, which Yannakakis has modified to test whether a hypergraph is acyclic. Here we develop a simplified linear-time test for graph chordality and hypergraph acyclicity. The test uses a new kind of graph (and hypergraph) search, which we call maximum cardinality search A variant of the method gives a way to selectively reduce acyclic hypergraphs, which is needed for evaluating queries in acyclic relational data bases.
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Citations
Cited by
(1988) · Cited by 16,582
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Kaess, M., Johannsson, H., Roberts, R., Ila, V., Leonard, J. J., & Dellaert, F. (2012) · The International Journal of Robotics Research · doi:10.1177/0278364911430419 · Cited by 1,362
Identifying the Minimal Transversals of a Hypergraph and Related Problems
Eiter, T., & Gottlob, G. (1995) · SIAM Journal on Computing · doi:10.1137/s0097539793250299 · Cited by 437
Pardalos, P. M., & Xue, J. (1994) · Journal of Global Optimization · doi:10.1007/bf01098364 · Cited by 382
Elements of Relational Database Theory
KANELLAKIS, P. C. (1990) · Formal Models and Semantics · doi:10.1016/b978-0-444-88074-1.50022-6 · Cited by 259
Metadata
- Authors
- Tarjan, R. E., & Yannakakis, M.
- Venue
- SIAM Journal on Computing
- Published
- 1984-08
- Volume
- 13
- Issue
- 3
- Pages
- 566-579
- ISSN
- 0097-5397 (ISSN-L)
- 1095-7111
- OpenAlex
- W1991477862
- Cited by
- 1,058
- References
- 0
- FWCI
- 16.69
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Simple Linear-Time Algorithms to Test Chordality of Graphs, Test Acyclicity of Hypergraphs, and Selectively Reduce Acyclic Hypergraphs. https://app.cochat.ai/papers/10.1137/0213035
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- Tarjan, R. E., & Yannakakis, M. (1984). Simple Linear-Time Algorithms to Test Chordality of Graphs, Test Acyclicity of Hypergraphs, and Selectively Reduce Acyclic Hypergraphs. SIAM Journal on Computing. https://doi.org/10.1137/0213035
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Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
