The geometric generalized minimum spanning tree problem with grid clustering

C. Feremans, A. Grigoriev, R.A. Sitters

    Research output: Contribution to journalArticleAcademicpeer-review

    10 Citations (Scopus)


    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 -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
    Journal4OR : A Quarterly Journal of Operations Research
    Issue number4
    Publication statusPublished - 2006


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