The geometric generalized minimum spanning tree problem with grid clustering

Corinne Feremans, Alexander Grigoriev*, René Sitters

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


This paper is concerned with a special case of the generalized minimum spanning tree problem. The problem is defined on an undirected graph, where the vertex set is partitioned into clusters, and non-negative costs are associated with the edges. The problem is to find a tree of minimum cost containing at least one vertex in each cluster. We consider a geometric case of the problem where the graph is complete, all vertices are situated in the plane, and Euclidean distance defines the edge cost. We prove that the problem is strongly NP-hard even in the case of a special structure of the clustering called grid clustering. We construct an exact exponential time dynamic programming algorithm and, based on this dynamic programming algorithm, we develop a polynomial time approximation scheme for the problem with grid clustering.

Original languageEnglish
Pages (from-to)319-329
Number of pages11
Issue number4
Publication statusPublished - 2006


  • Approximations
  • Complexity
  • Generalized minimum spanning tree
  • Grid clustering


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