Consider the Differentiated Set Coverage Problem: HE Input: n items, U (1,2,...,n), coverage requirements of the...

 

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Consider the Differentiated Set Coverage Problem: HE Input: n items, U (1,2,...,n), coverage requirements of the items f (ft. ff). m sets, S₁, S₂. S. price of the sets p (PPP) Let x (₁111) be the selection decisions of the sets, z, € (0, 1). Output: A minimum price selection x of the sets S₁, S., S, that can cover the items in U at least f times. Ex: Let n-6 and U-(1,2,3,4,5) having coverage requirements f= (1,2,1,2,1), Let m = 5 and S₁ (1,2), S (2,3,4), S₁ (2,5), S (3,4), Ss= (1,4) with prices p (5,6, 10,2,4). I For instance, item =2 € U should be covered by at least fa-2 different sets S. We note that item 2 can be covered by S, with price p₁-5, by S, with price pa 6 and by S with price p₁-10. 1. Determine a greedy selection rule for the sets. Design a greedy algorithm for the Differentiated Set Coveruge Problem and report the pseudocode. 2. Discuss the time complexity of your greedy algorithm. Is it efficient? Can your algorithm find the optimum solution? 3. Implement your algorithm in Python. Use the input given in the example and report the console outputs and your Python code scripts. Consider the Differentiated Set Coverage Problem: HE Input: n items, U (1,2,...,n), coverage requirements of the items f (ft. ff). m sets, S₁, S₂. S. price of the sets p (PPP) Let x (₁111) be the selection decisions of the sets, z, € (0, 1). Output: A minimum price selection x of the sets S₁, S., S, that can cover the items in U at least f times. Ex: Let n-6 and U-(1,2,3,4,5) having coverage requirements f= (1,2,1,2,1), Let m = 5 and S₁ (1,2), S (2,3,4), S₁ (2,5), S (3,4), Ss= (1,4) with prices p (5,6, 10,2,4). I For instance, item =2 € U should be covered by at least fa-2 different sets S. We note that item 2 can be covered by S, with price p₁-5, by S, with price pa 6 and by S with price p₁-10. 1. Determine a greedy selection rule for the sets. Design a greedy algorithm for the Differentiated Set Coveruge Problem and report the pseudocode. 2. Discuss the time complexity of your greedy algorithm. Is it efficient? Can your algorithm find the optimum solution? 3. Implement your algorithm in Python. Use the input given in the example and report the console outputs and your Python code scripts.

Answer rating: 100% (QA)

Greedy Selection Rule A possible greedy selection rule for this problem could be selecting sets that cover the most uncovered items based on their respective prices The algorithm should iteratively ch... View the full answer