Optimal arrangement of data in a tree directory: [Discrete Appl. Math 113 (2001) 243–253]

We define the decision problem DATA ARRANGEMENT, which involves arranging the vertices of a graph G at the leaves of a d-ary tree so that a weighted sum of the distances between pairs of vertices measured with respect to the tree topology is at most a given value. We show that DATA ARRANGEMENT is strongly NP-complete for any fixed d⩾2 and explain the connection between DATA ARRANGEMENT and arranging data in a particular form of distributed directory.