I just want the starting lead on how I should approach the problem of minimizing a given boolean expression of 4 variables and constructing a k-map based on that and accordingly simplifying the expression. (without Quine McCluskey Algo)

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do you want an algorithm for K Map ?

Do you mean how to find the right rectangles in the table?

I guess this problem is computationally quite hard (after all the whole problem is NP), even though humans can almost instantly solve it for a 4x4 matrix.

As an algorithm I would implement a complete search (which should be fast for 4x4) over all possible rectangles. Maybe you can improve runtime by some pruning.

thank you… and your intuition was infact correct…

for reference yes…