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Mathematical Programming

, Volume 28, Issue 3, pp 271–287 | Cite as

A dual ascent approach for steiner tree problems on a directed graph

  • Richard T. Wong
Article

Abstract

The Steiner tree problem on a directed graph (STDG) is to find a directed subtree that connects a root node to every node in a designated node setV. We give a dual ascent procedure for obtaining lower bounds to the optimal solution value. The ascent information is also used in a heuristic procedure for obtaining feasible solutions to the STDG. Computational results indicate that the two procedures are very effective in solving a class of STDG's containing up to 60 nodes and 240 directed/120 undirected arcs.

The directed spanning tree and uncapacitated plant location problems are special cases of the STDG. Using these relationships, we show that our ascent procedure can be viewed as a generalization ofboth the Chu-Liu-Edmonds directed spanning tree algorithm and the Bilde-Krarup-Erlenkotter ascent algorithm for the plant location problem. The former comparison yields a dual ascent interpretation of the steps of the directed spanning tree algorithm.

Key words

Steiner Tree Problem on a Graph Dual Ascent Method Directed Spanning Tree Algorithm 

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Copyright information

© The Mathematical Programming Society Inc. 1984

Authors and Affiliations

  • Richard T. Wong
    • 1
  1. 1.Purdue UniversityWest LafayetteUSA

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