The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Algorithmic Aspects of Vertex Elimination on Graphs
Abstract
We consider a graph-theoretic elimination process which is related to performing Gaussian elimination on sparse symmetric positive definite systems of linear equations. We give a new linear-time algorithm to calculate the fill-in produced by any elimination ordering, and we give two new related algorithms for finding orderings with special properties. One algorithm, based on breadth-first search, finds a perfect elimination ordering, if any exists, in $O(n + e)$ time, if the problem graph has n vertices and e edges. An extension of this algorithm finds a minimal (but not necessarily minimum) ordering in $O(ne)$ time. We conjecture that the problem of finding a minimum ordering is NP-complete
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Citations
Cites
The complexity of theorem-proving procedures
Cook, S. A. (1971) · Proceedings of the third annual ACM symposium on Theory of computing - STOC '71 · doi:10.1145/800157.805047 · Cited by 6,385
Gaussian elimination is not optimal
Strassen, V. (1969) · Numerische Mathematik · doi:10.1007/bf02165411 · Cited by 2,509
Cited by
Booth, K. S., & Lueker, G. S. (1976) · Journal of Computer and System Sciences · doi:10.1016/s0022-0000(76)80045-1 · Cited by 1,488
Self-citationLipton, R. J., Rose, D. J., & Tarjan, R. E. (1979) · SIAM Journal on Numerical Analysis · doi:10.1137/0716027 · Cited by 560
Self-citationPardalos, P. M., & Xue, J. (1994) · Journal of Global Optimization · doi:10.1007/bf01098364 · Cited by 382
Finding a Maximum Clique in an Arbitrary Graph
Balas, E., & Yu, C. S. (1986) · SIAM Journal on Computing · doi:10.1137/0215075 · Cited by 295
Toward Quantum Gate-Model Heuristics for Real-World Planning Problems
Stollenwerk, T., Hadfield, S., & Wang, Z. (2020) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2020.3030609 · Cited by 29
Metadata
- Authors
- Rose, D. J., Tarjan, R. E., & Lueker, G. S.
- Venue
- SIAM Journal on Computing
- Published
- 1976-06
- Volume
- 5
- Issue
- 2
- Pages
- 266-283
- ISSN
- 0097-5397 (ISSN-L)
- 1095-7111
- OpenAlex
- W2086119402
- Cited by
- 1,203
- References
- 2
- FWCI
- 9.13
- Type
- journal article
- Language
- en
- Open access
- closed
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- Rose, D. J., Tarjan, R. E., & Lueker, G. S. (1976). Algorithmic Aspects of Vertex Elimination on Graphs. SIAM Journal on Computing. https://doi.org/10.1137/0205021
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