GREEDY ALGORITHM PROBLEM:

Given subsets S1, S2, , Sn of a set S of points and an integer m, a maximum mcover is a collection of m of the subsets that covers the maximum number of points of S. Give a greedy algorithm that achieves approximation ratio 11/e; i.e., let y be the maximum number of points that can be covered by m subsets and x be the number of points that are covered by the m subsets generated by your algorithm, then give a greedy algorithm such that x (1 1/e)y.

Some useful hints:

You may want to use the inequality (1 1/m) m 1/e for integer m 1.

You may want to use induction at some point.

PLEASE SHOW ALL WORK STEPS. i AM TRYING TO UNDERSTAND HOW TO FIND THE SOLUTION TO THESE PROBLEMS