Santa is worried about his employee relations, since christmas preparations have led to a lot of overtime. To make sure all the elves are happy, he wants to recruit some of them as complaint officers, with weekly meetings to report any complaints or worries to him. His worker elves W are pretty busy already, so Santa wants to task no more than k elves with this additional workload. Still, Santa wants to make sure that for as many elves e W as possible, at least one of his friends (whose identities he knows) is a complaint officer. 1. Give an intuitive greedy algorithm that outputs k elves that will serve as compliant officers. 2. Prove that for large numbers of k the algorithm approximates a solution with ratio no more than (1 1/e ).