Rare Siblings Speed-Up Deterministic Detection and Counting of Small Pattern Graphs
(2019) 22nd International Symposium, FCT 2019, Copenhagen, Denmark, August 12-14 In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 11651. p.322-334- Abstract
We consider a class of pattern graphs on (formula presented) vertices that have q-2 distinguished vertices with equal neighborhood in the remaining two vertices. Two pattern graphs in this class are siblings if they differ by some edges connecting the distinguished vertices. In particular, we show that if induced copies of siblings to a pattern graph in such a class are rare in the host graph then one can detect the pattern graph relatively efficiently. For example, we infer that if there are (formula presented) induced copies of a diamond (i.e., a graph on four vertices missing a single edge to be complete) in the host graph, then an induced copy of the complete graph on four vertices, K:4 as well as an induced copy of the cycle on... (More)
We consider a class of pattern graphs on (formula presented) vertices that have q-2 distinguished vertices with equal neighborhood in the remaining two vertices. Two pattern graphs in this class are siblings if they differ by some edges connecting the distinguished vertices. In particular, we show that if induced copies of siblings to a pattern graph in such a class are rare in the host graph then one can detect the pattern graph relatively efficiently. For example, we infer that if there are (formula presented) induced copies of a diamond (i.e., a graph on four vertices missing a single edge to be complete) in the host graph, then an induced copy of the complete graph on four vertices, K:4 as well as an induced copy of the cycle on four vertices, C:4 can be deterministically detected in (formula presented) time. Note that the fastest known algorithm for K:4 and the fastest known deterministic algorithm for C:4 run in (formula presented) time. We also show that if there is a family of siblings whose induced copies in the host graph are rare then there are good chances to determine the numbers of occurrences of induced copies for all pattern graphs on q vertices relatively efficiently.
(Less)
- author
- Kowaluk, Mirosław and Lingas, Andrzej LU
- organization
- publishing date
- 2019-01-01
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Fundamentals of Computation Theory : 22nd International Symposium, FCT 2019, Proceedings - 22nd International Symposium, FCT 2019, Proceedings
- series title
- Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
- editor
- Gąsieniec, Leszek Antoni ; Jansson, Jesper and Levcopoulos, Christos
- volume
- 11651
- pages
- 13 pages
- publisher
- Springer
- conference name
- 22nd International Symposium, FCT 2019, Copenhagen, Denmark, August 12-14
- conference location
- Copenhagen, Denmark
- conference dates
- 2019-08-22 - 2019-08-24
- external identifiers
-
- scopus:85070616029
- ISSN
- 1611-3349
- 0302-9743
- ISBN
- 9783030250263
- 9783030250270
- DOI
- 10.1007/978-3-030-25027-0_22
- language
- English
- LU publication?
- yes
- id
- 867da6fb-eaf7-424f-8165-5731405be5cf
- date added to LUP
- 2019-08-26 09:58:59
- date last changed
- 2024-03-19 19:21:18
@inproceedings{867da6fb-eaf7-424f-8165-5731405be5cf,
abstract = {{<p>We consider a class of pattern graphs on (formula presented) vertices that have q-2 distinguished vertices with equal neighborhood in the remaining two vertices. Two pattern graphs in this class are siblings if they differ by some edges connecting the distinguished vertices. In particular, we show that if induced copies of siblings to a pattern graph in such a class are rare in the host graph then one can detect the pattern graph relatively efficiently. For example, we infer that if there are (formula presented) induced copies of a diamond (i.e., a graph on four vertices missing a single edge to be complete) in the host graph, then an induced copy of the complete graph on four vertices, K:4 as well as an induced copy of the cycle on four vertices, C:4 can be deterministically detected in (formula presented) time. Note that the fastest known algorithm for K:4 and the fastest known deterministic algorithm for C:4 run in (formula presented) time. We also show that if there is a family of siblings whose induced copies in the host graph are rare then there are good chances to determine the numbers of occurrences of induced copies for all pattern graphs on q vertices relatively efficiently.</p>}},
author = {{Kowaluk, Mirosław and Lingas, Andrzej}},
booktitle = {{Fundamentals of Computation Theory : 22nd International Symposium, FCT 2019, Proceedings}},
editor = {{Gąsieniec, Leszek Antoni and Jansson, Jesper and Levcopoulos, Christos}},
isbn = {{9783030250263}},
issn = {{1611-3349}},
language = {{eng}},
month = {{01}},
pages = {{322--334}},
publisher = {{Springer}},
series = {{Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)}},
title = {{Rare Siblings Speed-Up Deterministic Detection and Counting of Small Pattern Graphs}},
url = {{http://dx.doi.org/10.1007/978-3-030-25027-0_22}},
doi = {{10.1007/978-3-030-25027-0_22}},
volume = {{11651}},
year = {{2019}},
}