4TH International Congress on Technology - Engineering & SCIENCE - Kuala Lumpur - Malaysia (2017-08-05)

An Optimal Level Of Adding Relations With Long Lengths In A Pyramid Organization Structure
We have studied a model of adding relations between one member and every other member of the same level of a pyramid organization structure for the purpose of revealing optimal additional relations. The pyramid organization structure can be expressed as a rooted tree, if we let nodes and edges in the rooted tree correspond to members and relations between members in the organization respectively. Then the pyramid organization structure is characterized by the number of subordinates of each member, that is, the number of children of each node and the number of levels in the organization, that is, the height of the rooted tree [1]. For a model of adding edges between one node and every other node of the same depth N in a complete binary tree of height H, we have obtained an optimal depth to maximize the total shortening distance which is the sum of shortened lengths of shortest paths between every pair of all nodes by adding edges [2, 3]. A complete binary tree is a rooted tree in which all leaves have the same depth and all internal nodes have two children. Moreover maximizing the total shortening distance means that the communication of information between every member in the organization becomes the most efficient. This model is expressed as all edges have the same length. However, we should consider that adding edges differ from those of complete binary tree in length. This study proposes a model of adding edges between one node and every other node of the same depth N (N = 1, 2, ..., H) in a complete binary tree of height H (H = 1, 2, ...) when adding edges are longer than those of complete binary tree. The lengths of adding edges are L (1 < L < 2) while those of edges of complete binary tree are 1. The total shortening distance to obtain the optimal depth N* maximizing the total shortening distance is formulated. Furthermore, the total shortening distance of this model is illustrated with numerical examples.
Kiyoshi Sawada