Diversities and the Geometry of Hypergraphs.
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| Title: | Diversities and the Geometry of Hypergraphs. |
|---|---|
| Authors: | Bryant, David1 david.bryant@otago.ac.nz, Tupper, Paul F.2 pft3@math.sfu.ca |
| Source: | Discrete Mathematics & Theoretical Computer Science (DMTCS). 2014, Vol. 16 Issue 2, p1-20. 20p. |
| Subjects: | Fuzzy hypergraphs, Embeddings (Mathematics), Geometry, Mathematical optimization, Data analysis, Tree graphs, Graphic methods |
| Abstract: | The embedding of finite metrics in l1 has become a fundamental tool for both combinatorial optimization and largescale data analysis. One important application is to network flow problems as there is close relation between max-flow min-cut theorems and the minimal distortion embeddings of metrics into l1. Here we show that this theory can be generalized to a larger set of combinatorial optimization problems on both graphs and hypergraphs. This theory is not built on metrics and metric embeddings, but on diversities, a type of multi-way metric introduced recently by the authors. We explore diversity embeddings, l1 diversities, and their application to Steiner Tree Packing and Hypergraph Cut problems. [ABSTRACT FROM AUTHOR] |
| Copyright of Discrete Mathematics & Theoretical Computer Science (DMTCS) is the property of Discrete Mathematics & Theoretical Computer Science DMTCS 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 | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 97751238 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Diversities and the Geometry of Hypergraphs. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Bryant%2C+David%22">Bryant, David</searchLink><relatesTo>1</relatesTo><i> david.bryant@otago.ac.nz</i><br /><searchLink fieldCode="AR" term="%22Tupper%2C+Paul+F%2E%22">Tupper, Paul F.</searchLink><relatesTo>2</relatesTo><i> pft3@math.sfu.ca</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Discrete+Mathematics+%26+Theoretical+Computer+Science+%28DMTCS%29%22">Discrete Mathematics & Theoretical Computer Science (DMTCS)</searchLink>. 2014, Vol. 16 Issue 2, p1-20. 20p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Fuzzy+hypergraphs%22">Fuzzy hypergraphs</searchLink><br /><searchLink fieldCode="DE" term="%22Embeddings+%28Mathematics%29%22">Embeddings (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Geometry%22">Geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Data+analysis%22">Data analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Tree+graphs%22">Tree graphs</searchLink><br /><searchLink fieldCode="DE" term="%22Graphic+methods%22">Graphic methods</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The embedding of finite metrics in l1 has become a fundamental tool for both combinatorial optimization and largescale data analysis. One important application is to network flow problems as there is close relation between max-flow min-cut theorems and the minimal distortion embeddings of metrics into l1. Here we show that this theory can be generalized to a larger set of combinatorial optimization problems on both graphs and hypergraphs. This theory is not built on metrics and metric embeddings, but on diversities, a type of multi-way metric introduced recently by the authors. We explore diversity embeddings, l1 diversities, and their application to Steiner Tree Packing and Hypergraph Cut problems. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Discrete Mathematics & Theoretical Computer Science (DMTCS) is the property of Discrete Mathematics & Theoretical Computer Science DMTCS 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: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 20 StartPage: 1 Subjects: – SubjectFull: Fuzzy hypergraphs Type: general – SubjectFull: Embeddings (Mathematics) Type: general – SubjectFull: Geometry Type: general – SubjectFull: Mathematical optimization Type: general – SubjectFull: Data analysis Type: general – SubjectFull: Tree graphs Type: general – SubjectFull: Graphic methods Type: general Titles: – TitleFull: Diversities and the Geometry of Hypergraphs. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Bryant, David – PersonEntity: Name: NameFull: Tupper, Paul F. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: 2014 Type: published Y: 2014 Identifiers: – Type: issn-print Value: 13658050 Numbering: – Type: volume Value: 16 – Type: issue Value: 2 Titles: – TitleFull: Discrete Mathematics & Theoretical Computer Science (DMTCS) Type: main |
| ResultId | 1 |
