8.1. 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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the answer to your question would be something called hertz. the unit of measurement called a hertz, which is one cycle per second, is used to measure clock speed. within one cycle, your computer processes, refreshes, or updates itself to the changes that it is going through. in the case of computer clock speed, one hertz equals one tick per second. the clock speed of computers is usually measured in megahertz (mhz) or gigahertz (ghz)