Optimization versus search. Recall the traveling salesman problem:
TSP
Input: A matrix of distances; a budget b
Output: A tour which passes through all the cities and has length ≤ b, if such a tour exists.
The optimization version of this problem asks directly for the shortest tour.
TSP-OPT
Input: A matrix of distances
Output: The shortest tour which passes through all the cities.
Show that if TSP can be solved in polynomial time, then so can TSP-OPT.
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