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Steiner Minimum Trees in Uniform Orientation Metrics

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Book cover Steiner Trees in Industry

Part of the book series: Combinatorial Optimization ((COOP,volume 11))

Abstract

Let N be a set of points in the plane. Informally, the Steiner tree problem asks us to construct a network, known as a Steiner minimum network or Steiner minimum tree, interconnecting the points in N, such that the network has the shortest length possible with respect to a given distance function. Unlike minimum spanning trees, a Steiner minimum tree may contain vertices of degree 3 or more not in N. These points are usually referred to as Steiner points, and the inclusion of these points makes the Steiner problem an NP-hard problem.

Research partially supported by a grant from the Australian Research Council

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, The University of Melbourne, VIC, 3010, Australia

    Marcus Brazil

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  1. Marcus Brazil
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Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN, USA

    Xiu Zhen Cheng  & Ding-Zhu Du  & 

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Brazil, M. (2001). Steiner Minimum Trees in Uniform Orientation Metrics. In: Cheng, X.Z., Du, DZ. (eds) Steiner Trees in Industry. Combinatorial Optimization, vol 11. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0255-1_1

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  • DOI: https://doi.org/10.1007/978-1-4613-0255-1_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7963-8

  • Online ISBN: 978-1-4613-0255-1

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