Concatenation-based greedy heuristics for the Euclidean Steiner tree problem

Concatenation-based greedy heuristics for the Euclidean Steiner tree problem

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Article ID: iaor20011466
Country: United States
Volume: 25
Issue: 4
Start Page Number: 418
End Page Number: 437
Publication Date: Dec 1999
Journal: Algorithmica
Authors: ,
Keywords: heuristics
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.

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