Concatenation-Based Greedy Heuristics for the Euclidean Steiner Tree Problem

Martin Tvede Zachariasen, P. Winter

Research output: Journal Article or Conference Article in JournalJournal articleResearchpeer-review

Abstract

We present a class of O(n log n) heuristics for the Steiner tree problem in the Euclidean plane. These heuristics identify a small number of subsets with few, geometrically close, terminals using minimum spanning trees and other well-known structures from computational geometry: Delaunay triangulations, Gabriel graphs, relative neighborhood graphs, and higher-order Voronoi diagrams. Full Steiner trees of all these subsets are sorted according to some appropriately chosen measure of quality. A tree spanning all terminals is constructed using greedy concatenation. New heuristics are compared with each other and with heuristics from the literature by performing extensive computational experiments on both randomly generated and library problem instances.
Original languageEnglish
JournalAlgorithmica
Volume25
Pages (from-to)418-437
ISSN0178-4617
Publication statusPublished - 1999
Externally publishedYes

Keywords

  • Steiner Tree Problem
  • Euclidean Plane
  • Heuristics
  • Minimum Spanning Trees
  • Delaunay Triangulations

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