A model of placing liaisons in multi-levels of an organization structure of a complete binary tree minimizing total distance

This paper proposes a model of placing liaisons in multi-levels of a pyramid organization structure such that the communication of information between every member in the organization becomes the most efficient. When L nodes of liaisons which get adjacent to all nodes at each depth of L depths are placed in a complete binary tree of height H, an optimal set of depths {N₁, N₂,..., N_L}(H ≥ N₁ > N₂ >... > N_L ≥ 2) is obtained by minimizing the total distance which is the sum of lengths of shortest paths between every pair of all nodes in the complete binary tree. It is shown that {N₁, N₂,..., N_L}* = {H, H-1,..., H-L+1}.