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Computing the Maximum using (min, +) Formulas

We study computation by formulas over (min,+). We consider the 
computation of max{x_1,...,x_n} over N as a difference of 
(min,+) formulas, and show that size n + n \log n is sufficient 
and necessary. Our proof also shows that any (min,+) formula 
computing the minimum of all sums of n-1 out of n variables must 
have n \log n leaves; this too is tight. Our proofs use a 
complexity measure for (min,+) functions based on minterm-like 
behaviour and on the entropy of an associated graph.