Problem Statement. Consider the Generalized Minimum Spanning Tree

This paper is concerned with a special case of the Generalized Mini-mum Spanning Tree Problem. The Generalized Minimum Spanning Tree Problem is defined on an undirected graph, where the vertex set is parti-tioned into clusters, and non-negative costs are associated with the edges. The problem is to find a tree of minimum cost containing exactly one ver-tex 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 admits PTAS if restricted to grid clustering