Advanced

A fast deterministic detection of small pattern graphs in graphs without large cliques

Kowaluk, Mirosław and Lingas, Andrzej LU (2017) 11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017 In WALCOM: Algorithms and Computation - 11th International Conference and Workshops, WALCOM 2017, Proceedings 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).

(Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Induced subgraph isomorphism, Matrix multiplication, Time complexity, Witnesses for boolean matrix product
in
WALCOM: Algorithms and Computation - 11th International Conference and Workshops, WALCOM 2017, Proceedings
volume
10167 LNCS
pages
11 pages
publisher
Springer Verlag
conference name
11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017
external identifiers
  • scopus:85014185907
  • wos:000413067200017
ISSN
03029743
16113349
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
2018-01-16 13:24:52
@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         = {03029743},
  keyword      = {Induced subgraph isomorphism,Matrix multiplication,Time complexity,Witnesses for boolean matrix product},
  language     = {eng},
  pages        = {217--227},
  publisher    = {Springer Verlag},
  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},
  volume       = {10167 LNCS},
  year         = {2017},
}