25. For the -synchronizer, significant flexibility can be achieved by varying a parameter k that is used to give a bound on Lc (sum of

25. For the γ-synchronizer, significant flexibility can be achieved by varying a parameter k that is used to give a bound on Lc (sum of the number of tree edges and clustering edges) and hc

(maximum height of any tree in any cluster). Visually, this parameter determines the flatness of the cluster hierarchy.

Show that for every k, 2 ≤ k < n, a clustering scheme can be designed so as to satisfy the following bounds: (1) Lc < k · n, and (2) hc ≤ (log n)/(log k).