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Finding and counting patterns in sparse graphs.

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Title:	Finding and counting patterns in sparse graphs.
Authors:	Komarath, Balagopal¹ (AUTHOR) bkomarath@rbgo.in, Kumar, Anant¹ (AUTHOR) kumar_anant@iitgn.ac.in, Mishra, Suchismita^1,2 (AUTHOR) suchismitamishra6@gmail.com, Sethia, Aditi¹ (AUTHOR) aditi.sethia@iitgn.ac.in
Source:	Journal of Computer & System Sciences. May2026, Vol. 157, pN.PAG-N.PAG. 1p.
Subjects:	Sparse graphs, Algorithms, Graph theory, Polynomial time algorithms
Abstract:	We consider algorithms for finding and counting small, fixed graphs in sparse host graphs. In the non-sparse setting, the parameters treedepth and treewidth play a crucial role in fast, constant-space and polynomial-space algorithms respectively. We discover two new parameters that we call matched treedepth and matched treewidth. We show that, for many patterns, finding and counting patterns with low matched treedepth and low matched treewidth can be done asymptotically faster than the existing algorithms when the host graphs are sparse. As an application to finding and counting fixed-size patterns, we discover O ˜ (m 3) -time.1 constant-space algorithms for graphs on at most 11 edges and O ˜ (m 2) -time, polynomial-space algorithms for graphs on at most 9 edges.2 [ABSTRACT FROM AUTHOR]
	Copyright of Journal of Computer & System Sciences is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database:	Engineering Source

FullText	Text: Availability: 0
Header	DbId: egs DbLabel: Engineering Source An: 191296147 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0
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Items	– Name: Title Label: Title Group: Ti Data: Finding and counting patterns in sparse graphs. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Komarath%2C+Balagopal%22">Komarath, Balagopal</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> bkomarath@rbgo.in</i><br /><searchLink fieldCode="AR" term="%22Kumar%2C+Anant%22">Kumar, Anant</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> kumar_anant@iitgn.ac.in</i><br /><searchLink fieldCode="AR" term="%22Mishra%2C+Suchismita%22">Mishra, Suchismita</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> suchismitamishra6@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Sethia%2C+Aditi%22">Sethia, Aditi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> aditi.sethia@iitgn.ac.in</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Computer+%26+System+Sciences%22">Journal of Computer & System Sciences</searchLink>. May2026, Vol. 157, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Sparse+graphs%22">Sparse graphs</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomial+time+algorithms%22">Polynomial time algorithms</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We consider algorithms for finding and counting small, fixed graphs in sparse host graphs. In the non-sparse setting, the parameters treedepth and treewidth play a crucial role in fast, constant-space and polynomial-space algorithms respectively. We discover two new parameters that we call matched treedepth and matched treewidth. We show that, for many patterns, finding and counting patterns with low matched treedepth and low matched treewidth can be done asymptotically faster than the existing algorithms when the host graphs are sparse. As an application to finding and counting fixed-size patterns, we discover O ˜ (m 3) -time.1 constant-space algorithms for graphs on at most 11 edges and O ˜ (m 2) -time, polynomial-space algorithms for graphs on at most 9 edges.2 [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Computer & System Sciences is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo	BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.jcss.2025.103728 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Sparse graphs Type: general – SubjectFull: Algorithms Type: general – SubjectFull: Graph theory Type: general – SubjectFull: Polynomial time algorithms Type: general Titles: – TitleFull: Finding and counting patterns in sparse graphs. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Komarath, Balagopal – PersonEntity: Name: NameFull: Kumar, Anant – PersonEntity: Name: NameFull: Mishra, Suchismita – PersonEntity: Name: NameFull: Sethia, Aditi IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00220000 Numbering: – Type: volume Value: 157 Titles: – TitleFull: Journal of Computer & System Sciences Type: main
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