On the complexity of inverse convex ordered 1-median problem on the plane and on tree networks.
Saved in:
| Title: | On the complexity of inverse convex ordered 1-median problem on the plane and on tree networks. |
|---|---|
| Authors: | Nguyen, Kien Trung1 trungkien@ctu.edu.vn, Nguyen-Thu, Huong1 nthuong@ctu.edu.vn, Hung, Nguyen Thanh1 nthung@ctu.edu.vn |
| Source: | Mathematical Methods of Operations Research. Oct2018, Vol. 88 Issue 2, p147-159. 13p. 2 Diagrams. |
| Subjects: | Location theory (Geography), Planes (Hand tools), Trees, Multipliers (Mathematical analysis), Economic geography |
| Abstract: | An ordered median function is used in location theory to generalize a class of problems, including median and center problems. In this paper we consider the complexity of inverse ordered 1-median problems on the plane and on trees, where the multipliers are sorted nondecreasingly. Based on the convexity of the objective function, we prove that the problems with variable weights or variable coordinates on the line are NP-hard. Then we can directly get the NP-hardness result for the corresponding problem on the plane. We finally develop a cubic time algorithm that solves the inverse convex ordered 1-median problem on trees with relaxation on modification bounds. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematical Methods of Operations Research is the property of Springer Nature 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 |
|
Full text is not displayed to guests.
Login for full access.
|
|
| FullText | Links: – Type: pdflink Text: Availability: 1 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 132788985 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: On the complexity of inverse convex ordered 1-median problem on the plane and on tree networks. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Nguyen%2C+Kien+Trung%22">Nguyen, Kien Trung</searchLink><relatesTo>1</relatesTo><i> trungkien@ctu.edu.vn</i><br /><searchLink fieldCode="AR" term="%22Nguyen-Thu%2C+Huong%22">Nguyen-Thu, Huong</searchLink><relatesTo>1</relatesTo><i> nthuong@ctu.edu.vn</i><br /><searchLink fieldCode="AR" term="%22Hung%2C+Nguyen+Thanh%22">Hung, Nguyen Thanh</searchLink><relatesTo>1</relatesTo><i> nthung@ctu.edu.vn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematical+Methods+of+Operations+Research%22">Mathematical Methods of Operations Research</searchLink>. Oct2018, Vol. 88 Issue 2, p147-159. 13p. 2 Diagrams. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Location+theory+%28Geography%29%22">Location theory (Geography)</searchLink><br /><searchLink fieldCode="DE" term="%22Planes+%28Hand+tools%29%22">Planes (Hand tools)</searchLink><br /><searchLink fieldCode="DE" term="%22Trees%22">Trees</searchLink><br /><searchLink fieldCode="DE" term="%22Multipliers+%28Mathematical+analysis%29%22">Multipliers (Mathematical analysis)</searchLink><br /><searchLink fieldCode="DE" term="%22Economic+geography%22">Economic geography</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: An ordered median function is used in location theory to generalize a class of problems, including median and center problems. In this paper we consider the complexity of inverse ordered 1-median problems on the plane and on trees, where the multipliers are sorted nondecreasingly. Based on the convexity of the objective function, we prove that the problems with variable weights or variable coordinates on the line are NP-hard. Then we can directly get the NP-hardness result for the corresponding problem on the plane. We finally develop a cubic time algorithm that solves the inverse convex ordered 1-median problem on trees with relaxation on modification bounds. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematical Methods of Operations Research is the property of Springer Nature 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=132788985 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s00186-018-0632-6 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 13 StartPage: 147 Subjects: – SubjectFull: Location theory (Geography) Type: general – SubjectFull: Planes (Hand tools) Type: general – SubjectFull: Trees Type: general – SubjectFull: Multipliers (Mathematical analysis) Type: general – SubjectFull: Economic geography Type: general Titles: – TitleFull: On the complexity of inverse convex ordered 1-median problem on the plane and on tree networks. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Nguyen, Kien Trung – PersonEntity: Name: NameFull: Nguyen-Thu, Huong – PersonEntity: Name: NameFull: Hung, Nguyen Thanh IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2018 Type: published Y: 2018 Identifiers: – Type: issn-print Value: 14322994 Numbering: – Type: volume Value: 88 – Type: issue Value: 2 Titles: – TitleFull: Mathematical Methods of Operations Research Type: main |
| ResultId | 1 |
