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Question 1 : ( 5 0 pts ) Consider the Differentiated Set Coverage Problem: Input: n items, U = 1 , 2 , . .

Question 1: (50 pts) Consider the Differentiated Set Coverage Problem: Input: n items, U=1,2,..., n, coverage requirements of the items = f_1, f_2,..., f_n, m sets, S_1, S_2,..., S_m, price of the sets = p_1, p_2,..., p_m. Let = x_1, x_2,..., x_m be the selection decisions of the sets, x_i in {0,1}. Output: A minimum price selection x of the sets S_1, S_2,..., S_m that can cover the items in U at least times. Ex: Let n=5 and U=1,2,3,4,5 having coverage requirements =1,2,1,2,1. Let m=5 and S_1={1,2}, S_2={2,3,4}, S_3={2,5}, S_4={3,4}, S_5={1,4} with prices =5,6,10,2,4. For instance, item j=2 in U should be covered by at least f_2=2 different sets S_i. We note that item 2 can be covered by S_1 with price p_1=5, by S_2 with price p_2=6 and by S_3 with price p_3=10.1.(20 pts) Determine a greedy selection rule for the sets. Design a greedy algorithm for the Differentiated Set Coverage Problem and report the pseudocode. 2.(10 pts) Discuss the time complexity of your greedy algorithm. Is it efficient? Can your algorithm find the optimum solution? 3.(20 pts) Implement your algorithm in Java. Use the input given in the example and report the console outputs. Report your Java code scripts.

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