# MinMaxNN: minimum of MaxNN(G,H) over all subsets H of [n] with size r.
MinMaxNN:=proc(G,r) local n,i,c,mini,curr:
 n:=G[1]:
 c:=firstcomb(n,r):  
 mini:=MaxNN(G,c):   # check {1,..,r} first

 while nextcomb(c,n)<>FAIL do:   # check all other r-subsets of [n] and update the minimum if they are better
  c:=nextcomb(c,n):
  curr:=MaxNN(G,c):
  if curr < mini then:
   mini:=curr:
  fi:
 od:

 mini:
end: