Comment:
How do we know when to apply an optimal method and when to use an approximation method instead?
Follow-up:
Generally we want to solve a problem fast. Thus, if there is a fast optimal method (for a more precise notion of “fast”, please refer to Homework 5), then we should just use it. Now, a possibly difficult situation arises when we do not have a fast optimal method. For example, the optimal method requires exponential running time. In such a situation, we might need to forgo optimality but use a fast method that will give us an answer, possibly not optimal, but within a short period of time. For example, the “touring” (i.e., gossiping) problem is usually solved by a sub-optimal but fast method.
We had a subject in our syllabus of MCA second year or so .That subject was named Operational research which need to find best methods.It was an interesting subject for me.
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