An Optimal Placement of a Liaison with Short Communication Lengths Between Two Members of the Same Level in an Organization Structure of a Complete K-ary Tree

Abstract

This paper proposes a model of placing a liaison which forms relations to two members in the same level of a pyramid organization structure when lengths between the liaison and the other members are less than those between members except the liaison in the organization such that the communication of information between every member in the organization becomes the most efficient. For a model of adding a node of liaison which gets adjacent to two nodes with the same depth in a complete $K$-ary tree of height $H$ where the lengths of edges between the liaison and the other members are $L(0<L<1)$ while those of edges between members except the liaison are $1$, an optimal pair of two nodes to which the node of liaison gets adjacent is obtained by maximizing the total shortening distance which is the sum of shortening lengths of shortest paths between every pair of all nodes in the complete $K$-ary tree.