Optimal arrangement of data in a tree directory

Abstract

We define the decision problem {\textsc {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 {\textsc{data arrangement}} is strongly NP-complete for any fixed $d \ge 2$ and explain the connection between {\textsc{data arrangement}} and arranging data in a particular form of distributed directory.