A fast deterministic detection of small pattern graphs in graphs without large cliques
(2017) 11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017 In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 10167 LNCS. p.217-227- Abstract
We show that for several pattern graphs on four vertices (e.g., C4), their induced copies in host graphs with n vertices and no clique on k + 1 vertices can be deterministically detected in time Õ (nωkμ + n2k2), where Õ (f) stands for O(f(log f)c) for some constant c, and μ ≈ 0. 46530. The aforementioned pattern graphs have a pair of non-adjacent vertices whose neighborhoods are equal. By considering dual graphs, in the same asymptotic time, we can also detect four vertex pattern graphs, that have an adjacent pair of vertices with the same neighbors among the remaining vertices (e.g., K4), in host graphs with n vertices and no independent set on k + 1 vertices.... (More)
We show that for several pattern graphs on four vertices (e.g., C4), their induced copies in host graphs with n vertices and no clique on k + 1 vertices can be deterministically detected in time Õ (nωkμ + n2k2), where Õ (f) stands for O(f(log f)c) for some constant c, and μ ≈ 0. 46530. The aforementioned pattern graphs have a pair of non-adjacent vertices whose neighborhoods are equal. By considering dual graphs, in the same asymptotic time, we can also detect four vertex pattern graphs, that have an adjacent pair of vertices with the same neighbors among the remaining vertices (e.g., K4), in host graphs with n vertices and no independent set on k + 1 vertices. By using the concept of Ramsey numbers, we can extend our method for induced subgraph isomorphism to include larger pattern graphs having a set of independent vertices with the same neighborhood and nvertex host graphs without cliques on k+1 vertices (as well as the pattern graphs and host graphs dual to the aforementioned ones, respectively).
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- author
- Kowaluk, Mirosław and Lingas, Andrzej LU
- organization
- publishing date
- 2017
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Induced subgraph isomorphism, Matrix multiplication, Time complexity, Witnesses for boolean matrix product
- host publication
- WALCOM: Algorithms and Computation - 11th International Conference and Workshops, WALCOM 2017, Proceedings
- series title
- Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
- volume
- 10167 LNCS
- pages
- 11 pages
- publisher
- Springer
- conference name
- 11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017
- conference location
- Hsinchu, Taiwan
- conference dates
- 2017-03-29 - 2017-03-31
- external identifiers
-
- wos:000413067200017
- scopus:85014185907
- ISSN
- 16113349
- 03029743
- ISBN
- 9783319539249
- DOI
- 10.1007/978-3-319-53925-6_17
- language
- English
- LU publication?
- yes
- id
- 2b240aef-7f37-41e9-ad24-085acf5064b5
- date added to LUP
- 2017-03-15 12:38:55
- date last changed
- 2025-01-07 09:40:00
@inproceedings{2b240aef-7f37-41e9-ad24-085acf5064b5, abstract = {{<p>We show that for several pattern graphs on four vertices (e.g., C<sub>4</sub>), their induced copies in host graphs with n vertices and no clique on k + 1 vertices can be deterministically detected in time Õ (n<sup>ω</sup>k<sup>μ</sup> + n<sup>2</sup>k<sup>2</sup>), where Õ (f) stands for O(f(log f)<sup>c</sup>) for some constant c, and μ ≈ 0. 46530. The aforementioned pattern graphs have a pair of non-adjacent vertices whose neighborhoods are equal. By considering dual graphs, in the same asymptotic time, we can also detect four vertex pattern graphs, that have an adjacent pair of vertices with the same neighbors among the remaining vertices (e.g., K<sub>4</sub>), in host graphs with n vertices and no independent set on k + 1 vertices. By using the concept of Ramsey numbers, we can extend our method for induced subgraph isomorphism to include larger pattern graphs having a set of independent vertices with the same neighborhood and nvertex host graphs without cliques on k+1 vertices (as well as the pattern graphs and host graphs dual to the aforementioned ones, respectively).</p>}}, author = {{Kowaluk, Mirosław and Lingas, Andrzej}}, booktitle = {{WALCOM: Algorithms and Computation - 11th International Conference and Workshops, WALCOM 2017, Proceedings}}, isbn = {{9783319539249}}, issn = {{16113349}}, keywords = {{Induced subgraph isomorphism; Matrix multiplication; Time complexity; Witnesses for boolean matrix product}}, language = {{eng}}, pages = {{217--227}}, publisher = {{Springer}}, series = {{Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)}}, title = {{A fast deterministic detection of small pattern graphs in graphs without large cliques}}, url = {{http://dx.doi.org/10.1007/978-3-319-53925-6_17}}, doi = {{10.1007/978-3-319-53925-6_17}}, volume = {{10167 LNCS}}, year = {{2017}}, }