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THE ROLE OF STEINER HULLS IN THE SOLUTION TO STEINER TREE PROBLEMS.

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Title: THE ROLE OF STEINER HULLS IN THE SOLUTION TO STEINER TREE PROBLEMS.
Authors: Provan, J. Scott1
Source: Annals of Operations Research. 1991, Vol. 33 Issue 1-4, p537-548. 12p. 3 Diagrams.
Subjects: Steiner systems, Block designs, Decision trees, Decision making, Mathematical models, Euclidean algorithm, Operations research, Decision theory, Mathematical programming
Abstract: A Steiner tree problem on the plane is that of finding a minimum length Steiner tree connecting a given set K of terminals and lying within a given region R of the Euclidean plane; it includes as special cases the Euclidean Steiner minimal tree problem (ESMT), the rectilinear Steiner tree problem (RST), and the Steiner tree problem on graphs (STG). A Steiner hull for K in R generically refers to any subregion of R known to contain a Steiner tree. This paper gives a survey of the role of Steiner hulls in the Steiner tree problem. The significance of Steiner hulls in the efficient solution of Steiner tree problems is outlined, and then a compendium is given of the known Steiner hull constructions for ESMT, RST, and STG problems. [ABSTRACT FROM AUTHOR]
Copyright of Annals 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.)
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  Data: <searchLink fieldCode="DE" term="%22Steiner+systems%22">Steiner systems</searchLink><br /><searchLink fieldCode="DE" term="%22Block+designs%22">Block designs</searchLink><br /><searchLink fieldCode="DE" term="%22Decision+trees%22">Decision trees</searchLink><br /><searchLink fieldCode="DE" term="%22Decision+making%22">Decision making</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Euclidean+algorithm%22">Euclidean algorithm</searchLink><br /><searchLink fieldCode="DE" term="%22Operations+research%22">Operations research</searchLink><br /><searchLink fieldCode="DE" term="%22Decision+theory%22">Decision theory</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+programming%22">Mathematical programming</searchLink>
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  Data: A Steiner tree problem on the plane is that of finding a minimum length Steiner tree connecting a given set K of terminals and lying within a given region R of the Euclidean plane; it includes as special cases the Euclidean Steiner minimal tree problem (ESMT), the rectilinear Steiner tree problem (RST), and the Steiner tree problem on graphs (STG). A Steiner hull for K in R generically refers to any subregion of R known to contain a Steiner tree. This paper gives a survey of the role of Steiner hulls in the Steiner tree problem. The significance of Steiner hulls in the efficient solution of Steiner tree problems is outlined, and then a compendium is given of the known Steiner hull constructions for ESMT, RST, and STG problems. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Annals 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.)
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        Text: English
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      – SubjectFull: Steiner systems
        Type: general
      – SubjectFull: Block designs
        Type: general
      – SubjectFull: Decision trees
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      – SubjectFull: Decision making
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      – SubjectFull: Mathematical models
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      – SubjectFull: Euclidean algorithm
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      – SubjectFull: Operations research
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      – SubjectFull: Decision theory
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              Text: 1991
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