  A minimal permutation representation of a finite group G is a faithful G-set
with the smallest possible size. We study the structure of such representations
and show that for certain groups they may be obtained by a greedy construction.
In these situations (except when central involutions intervene) all minimal
permutation representations have the same set of orbit sizes. Using the same
ideas we also show that if the size d(G) of a minimal faithful G-set is at
least c|G| for some c>0 then d(G) = |G|/m + O(1) for an integer m, with the
implied constant depending on c.
