The DOI matches its Crossref record; 7 of the 7 references it cites were found in a registry or an index.
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
Abstract
In this paper, we give for constant k a linear-time algorithm that, given a graph $G = (V,E)$, determines whether the treewidth of G is at most k and, if so, finds a tree-decomposition of G with treewidth at most k. A consequence is that every minor-closed class of graphs that does not contain all planar graphs has a linear-time recognition algorithm. Another consequence is that a similar result holds when we look instead for path-decompositions with pathwidth at most some constant k.
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Cites
Graph minors. II. Algorithmic aspects of tree-width
Robertson, N., & Seymour, P. D. (1986) · Journal of Algorithms · doi:10.1016/0196-6774(86)90023-4 · Cited by 1,542
Graph Minors .XIII. The Disjoint Paths Problem
Robertson, N., & Seymour, P. D. (1995) · Journal of Combinatorial Theory, Series B · doi:10.1006/jctb.1995.1006 · Cited by 1,262
Complexity of Finding Embeddings in a k-Tree
Arnborg, S., Corneil, D. G., & Proskurowski, A. (1987) · SIAM Journal on Algebraic Discrete Methods · doi:10.1137/0608024 · Cited by 1,206
Graph minors. X. Obstructions to tree-decomposition
Robertson, N., & Seymour, P. D. (1991) · Journal of Combinatorial Theory, Series B · doi:10.1016/0095-8956(91)90061-n · Cited by 658
Linear time algorithms for NP-hard problems restricted to partial k-trees
Arnborg, S., & Proskurowski, A. (1989) · Discrete Applied Mathematics · doi:10.1016/0166-218x(89)90031-0 · Cited by 577
Efficient algorithms for combinatorial problems on graphs with bounded decomposability — A survey
Arnborg, S. (1985) · BIT · doi:10.1007/bf01934985 · Cited by 362
Leeuwen, J. V. (1990) · Elsevier eBooks · doi:10.1016/b978-0-444-88071-0.50015-1 · Cited by 88
Cited by
PARAMETERIZED COMPLEXITY THEORY
Niedermeier, R. (2006) · Invitation to Fixed-Parameter Algorithms · doi:10.1093/acprof:oso/9780198566076.003.0013 · Cited by 574
A differential approach to inference in Bayesian networks
Darwiche, A. (2003) · Journal of the ACM · doi:10.1145/765568.765570 · Cited by 470
Tree-Like Structure in Large Social and Information Networks
Adcock, A. B., Sullivan, B. D., & Mahoney, M. W. (2013) · 2013 IEEE 13th International Conference on Data Mining · doi:10.1109/icdm.2013.77 · Cited by 141
Adiabatic quantum programming: minor embedding with hard faults
Klymko, C., Sullivan, B. D., & Humble, T. S. (2014) · Quantum Information Processing · doi:10.1007/s11128-013-0683-9 · Cited by 99
Li, X., Wang, Y., Song, J., Liu, Y., Zhang, X., Zhou, K., & Li, C. (2020) · World Wide Web · doi:10.1007/s11280-019-00769-8 · Cited by 7
Metadata
- Authors
- Bodlaender, H. L.
- Venue
- SIAM Journal on Computing
- Published
- 1996-12
- Volume
- 25
- Issue
- 6
- Pages
- 1305-1317
- ISSN
- 0097-5397 (ISSN-L)
- 1095-7111
- OpenAlex
- W2059372025
- Cited by
- 1,542
- References
- 7
- FWCI
- 31.43
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth. https://app.cochat.ai/papers/10.1137/s0097539793251219
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- Bodlaender, H. L. (1996). A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth. SIAM Journal on Computing. https://doi.org/10.1137/s0097539793251219
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
