Approximation of convex curves with application to the bicriterial minimum cost flow problem.
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| Title: | Approximation of convex curves with application to the bicriterial minimum cost flow problem. |
|---|---|
| Authors: | Fruhwirth, B.1, Burkard, R. E.1, Rote, G.1 |
| Source: | European Journal of Operational Research. 10/16/89, Vol. 42 Issue 3, p326-338. 13p. 2 Diagrams, 4 Charts, 6 Graphs. |
| Subjects: | Approximation theory, Functional analysis, Piecewise linear topology, Manifolds (Mathematics), Differential geometry, Complex manifolds |
| Abstract: | An approximation of an explicitly or implicitly given convex curve in the plane is given by two piecewise linear 'outer' and 'inner' curves. To compute these, three rules for choosing the supporting points are proposed and it is shown for two of them that the projective distance between inner and outer approximation decreases quadratically with the number of supporting points. This method is applied to approximate the efficient point curve of the Bicriterial Minimum Cost Flow Problem, which is a piecewise linear convex curve that may have an exponential number of breakpoints in the worst case. [ABSTRACT FROM AUTHOR] |
| Copyright of European Journal of Operational Research 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 |
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| Header | DbId: egs DbLabel: Engineering Source An: 8513388 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Approximation of convex curves with application to the bicriterial minimum cost flow problem. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Fruhwirth%2C+B%2E%22">Fruhwirth, B.</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Burkard%2C+R%2E+E%2E%22">Burkard, R. E.</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Rote%2C+G%2E%22">Rote, G.</searchLink><relatesTo>1</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22European+Journal+of+Operational+Research%22">European Journal of Operational Research</searchLink>. 10/16/89, Vol. 42 Issue 3, p326-338. 13p. 2 Diagrams, 4 Charts, 6 Graphs. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Functional+analysis%22">Functional analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Piecewise+linear+topology%22">Piecewise linear topology</searchLink><br /><searchLink fieldCode="DE" term="%22Manifolds+%28Mathematics%29%22">Manifolds (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+geometry%22">Differential geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Complex+manifolds%22">Complex manifolds</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: An approximation of an explicitly or implicitly given convex curve in the plane is given by two piecewise linear 'outer' and 'inner' curves. To compute these, three rules for choosing the supporting points are proposed and it is shown for two of them that the projective distance between inner and outer approximation decreases quadratically with the number of supporting points. This method is applied to approximate the efficient point curve of the Bicriterial Minimum Cost Flow Problem, which is a piecewise linear convex curve that may have an exponential number of breakpoints in the worst case. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of European Journal of Operational Research 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.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/0377-2217(89)90443-8 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 13 StartPage: 326 Subjects: – SubjectFull: Approximation theory Type: general – SubjectFull: Functional analysis Type: general – SubjectFull: Piecewise linear topology Type: general – SubjectFull: Manifolds (Mathematics) Type: general – SubjectFull: Differential geometry Type: general – SubjectFull: Complex manifolds Type: general Titles: – TitleFull: Approximation of convex curves with application to the bicriterial minimum cost flow problem. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Fruhwirth, B. – PersonEntity: Name: NameFull: Burkard, R. E. – PersonEntity: Name: NameFull: Rote, G. IsPartOfRelationships: – BibEntity: Dates: – D: 16 M: 10 Text: 10/16/89 Type: published Y: 1989 Identifiers: – Type: issn-print Value: 03772217 Numbering: – Type: volume Value: 42 – Type: issue Value: 3 Titles: – TitleFull: European Journal of Operational Research Type: main |
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