The minimum routing cost spanning tree problem is a classic NP-hard problem, even for metric graphs. Given an edge-weighted graph, the problem asks for a spanning tree minimizing the sum of distances between all pairs of vertices. In this paper, we investigate a new variant named clustered minimum routing cost tree (CLUSTER MRCT) problem on metric graphs, in which the vertices are partitioned into clusters and the subtrees spanning clusters must be mutually disjoint in a feasible clustered spanning tree. We design a 2-approximation algorithm with time complexity O(n2) for CLUSTER MRCT, where n is the number of vertices of input graph.
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