An Optimal Placement of a Liaison between Two Levels in an Organization Structure of a Complete K-ary Tree

This paper proposes a model of placing a liaison which forms relations to two members of different levels in a pyramid organization structure such that the communication of information between every member in the organization becomes the most efficient. For the model of adding a node of liaison which gets adjacent to a node with a depth M and its descendant with a depth N in a complete K-ary tree of height H which can describe a pyramid organization structure with K subordinates, we obtained an optimal pair of depth (M, N)∗ which maximizes the sum of shortening lengths of the shortest paths between every pair of all nodes in the complete K-ary tree.