Grade of Service Steiner Trees in Series-Parallel Networks

  • Charles J. Colbourn
  • Guoliang Xue
Part of the Combinatorial Optimization book series (COOP, volume 6)


The grade of service Steiner tree problem is to determine the minimum total cost of an assignment of a grade of service to each link in a network, so that between each pair of nodes there is a path whose minimum grade of service is at least as large as the grade required at each of the end nodes. This problem has important applications in communication networks and in transportation. It generalizes the Steiner tree problem, in which there are two grades of service. When the network has n nodes and there are r grades of service, an algorithm to determine the cost of a grade of service Steiner tree is given which runs in O(r 3 n) time on series-parallel networks.


Steiner Tree Service Request Steiner Tree Problem Steiner Minimal Tree Minimum Total Cost 


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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Charles J. Colbourn
    • 1
  • Guoliang Xue
    • 1
  1. 1.Department of Computer ScienceUniversity of VermontBurlingtonUSA

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