Randomization for approximation 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? 1 cs 170, fall 2019 hw 12 p. raghavendra & s. rao (c) give an example of a max 3-sat instance where the optimal solution matches the number in (b)