A glob is an entity that can be attached to at most one other glob.
A glob that is not attached to any other glob is said to be a terminal glob.
For any glob g, one may trace a globular path from g
through attached globs to a terminal glob; the number of globs traversed in
a globular path from glob g is defined to be the length of the
globular path of g (for example, if g is a terminal glob
then its globular path has length 1, if glob a is attached to glob
b and b to c and c is terminal then the
globular path of a has length 3). All the globs which have a
globular path ending at the same terminal glob are said to be in the same
globular cluster. Globular clusters may be combined ONLY as follows:
attach the terminal glob of the smaller (fewer globs) cluster to the terminal
glob of the larger.
Start with n terminal globs (each by itself is a globular cluster).
Now, repeatedly pick two globular clusters and combine them. Show by
induction that the longest globular path is always less than
O(log(n)) in length.