# Oftentimes, extremely simple randomized algorithms can achieve reasonably good approximation factors.

###### Question:

Oftentimes, extremely simple randomized algorithms can achieve reasonably good approximation factors. (a) consider max 3-sat (given a set of 3-clauses, find the assignment that satisfies as many of them as possible). come up with a simple randomized algorithm that will achieve an approximation factor of 7 8 in expectation. that is, if the optimal solution satisfies k clauses, your algorithm should produce an assignment that satisfies at least 7 8 ∗ k clauses in expectation. you may assume that every clause contains exactly 3 distinct variables. (b) given an instance of max 3-sat with n clauses, what is the maximum number of clauses that are guaranteed to be solved in at least one assignment of variables?

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