Layers and matroids for the traveling salesman's paths.
Saved in:
| Title: | Layers and matroids for the traveling salesman's paths. |
|---|---|
| Authors: | Schalekamp, Frans1 fms9@cornell.edu, Sebő, András2 andras.sebo@grenoble-inp.fr, Traub, Vera1,3 traub@or.uni-bonn.de, van Zuylen, Anke4 anke@wm.edu |
| Source: | Operations Research Letters. Jan2018, Vol. 46 Issue 1, p60-63. 4p. |
| Subjects: | Layers (Computer graphics), Matroids, Linear programming, Polyhedral functions, Spanning trees |
| Abstract: | Abstract Gottschalk and Vygen proved that every solution of the subtour elimination linear program for traveling salesman paths is a convex combination of more and more restrictive "generalized Gao-trees". We give a short proof of this fact, as a layered convex combination of bases of a sequence of increasingly restrictive matroids. A strongly polynomial, combinatorial algorithm follows for finding this convex combination, which is a new tool offering polyhedral insight, already instrumental in recent results for the s − t path TSP. [ABSTRACT FROM AUTHOR] |
| Copyright of Operations Research Letters is the property of Elsevier B.V. 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: 134185082 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Layers and matroids for the traveling salesman's paths. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Schalekamp%2C+Frans%22">Schalekamp, Frans</searchLink><relatesTo>1</relatesTo><i> fms9@cornell.edu</i><br /><searchLink fieldCode="AR" term="%22Sebő%2C+András%22">Sebő, András</searchLink><relatesTo>2</relatesTo><i> andras.sebo@grenoble-inp.fr</i><br /><searchLink fieldCode="AR" term="%22Traub%2C+Vera%22">Traub, Vera</searchLink><relatesTo>1,3</relatesTo><i> traub@or.uni-bonn.de</i><br /><searchLink fieldCode="AR" term="%22van+Zuylen%2C+Anke%22">van Zuylen, Anke</searchLink><relatesTo>4</relatesTo><i> anke@wm.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Operations+Research+Letters%22">Operations Research Letters</searchLink>. Jan2018, Vol. 46 Issue 1, p60-63. 4p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Layers+%28Computer+graphics%29%22">Layers (Computer graphics)</searchLink><br /><searchLink fieldCode="DE" term="%22Matroids%22">Matroids</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+programming%22">Linear programming</searchLink><br /><searchLink fieldCode="DE" term="%22Polyhedral+functions%22">Polyhedral functions</searchLink><br /><searchLink fieldCode="DE" term="%22Spanning+trees%22">Spanning trees</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Abstract Gottschalk and Vygen proved that every solution of the subtour elimination linear program for traveling salesman paths is a convex combination of more and more restrictive "generalized Gao-trees". We give a short proof of this fact, as a layered convex combination of bases of a sequence of increasingly restrictive matroids. A strongly polynomial, combinatorial algorithm follows for finding this convex combination, which is a new tool offering polyhedral insight, already instrumental in recent results for the s − t path TSP. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Operations Research Letters is the property of Elsevier B.V. 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.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=134185082 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.orl.2017.11.002 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 4 StartPage: 60 Subjects: – SubjectFull: Layers (Computer graphics) Type: general – SubjectFull: Matroids Type: general – SubjectFull: Linear programming Type: general – SubjectFull: Polyhedral functions Type: general – SubjectFull: Spanning trees Type: general Titles: – TitleFull: Layers and matroids for the traveling salesman's paths. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Schalekamp, Frans – PersonEntity: Name: NameFull: Sebő, András – PersonEntity: Name: NameFull: Traub, Vera – PersonEntity: Name: NameFull: van Zuylen, Anke IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: Jan2018 Type: published Y: 2018 Identifiers: – Type: issn-print Value: 01676377 Numbering: – Type: volume Value: 46 – Type: issue Value: 1 Titles: – TitleFull: Operations Research Letters Type: main |
| ResultId | 1 |
