Adding Edges between One Node and Every Other Node with the Same Depth in a Complete K-ary Tree

Authors: Kiyoshi Sawada, Takashi Mitsuishi

Abstract:

This paper proposes a model of adding relations between members of the same level in a pyramid organization structure which is a complete K-ary tree such that the communication of information between every member in the organization becomes the most efficient. When edges between one node and every other node with the same depth N in a complete K-ary tree of height H are added, an optimal depth N* = H is obtained by minimizing the total path length which is the sum of lengths of shortest paths between every pair of all nodes.

Keywords: complete K-ary tree, organization structure, shortest path

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1335420

References:

[1] H. Koontz, C. O-Donnell, and H. Weihrich, Management, 7th Edition. New York: McGraw-Hill, 1980.
[2] N. Takahashi, "Sequential analysis of organization design: a model and a case of Japanese firms," European Journal of Operational Research, vol.36, pp.297-310, 1988.
[3] S. P. Robbins, Essentials of Organizational Behavior, 7th Edition. Upper Saddle River, NJ: Prentice Hall, 2003.
[4] Y. Takahara and M. Mesarovic, Organization Structure: Cybernetic Systems Foundation. New York: Kluwer Academic / Plenum Publishers, 2003.
[5] K. Sawada and R. Wilson, "Models of adding relations to an organization structure of a complete K-ary tree," European Journal of Operational Research, vol.174, pp.1491-1500, 2006.
[6] T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms, 2nd Edition. Cambridge, MA: MIT Press, 2001