In the MAX SAT problem, we are given a formula ?? with m clausesover n variables and we want to find a truth assignment thatsatisfies as many clauses as possible.
Here is a simple randomized algorithm for this problem.
for each variable do
set its value to either 0 or 1 by flipping a coin
end for
(a) Suppose that the j-th clause has kj literals. Give theexpected number of clauses satisfied by the above algorithm andprovide a lower bound for this number in terms of the inputparameters.
(b) Next assume that each clause contains exactly k literals.Give the expected number of clauses satisfied now and
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