Models of Adding Edges between the Root and Descendants in a Complete Binary Tree Minimizing Total Path Length

摘要

This paper proposes two models of adding relations to an organization structure which is a complete binary tree of height H: (i) a model of adding an edge between the root and one node of depth N and (ii) a model of adding edges between the root and all nodes of depth N. For each of the two models, an optimal depth N{sup}* is obtained by minimizing the total path length which is the sum of lengths of shortest paths between every pair of all nodes.