The role of Steiner hulls in the solution to Steiner tree problems

The role of Steiner hulls in the solution to Steiner tree problems

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Article ID: iaor19921092
Country: Switzerland
Volume: 33
Start Page Number: 537
End Page Number: 548
Publication Date: Nov 1991
Journal: Annals of Operations Research
Authors:
Keywords: Steiner problem
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.

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