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The set cover problem is as follows: provided a set S of subsets S1, Sm of the universal set U = {1,.....,n}, compute the smallest subset of subsets T ⊂ S such that ∪ti∈T ti = U. For instance, there exist following subsets, S1 = {1, 3, 5}, S2 = {2, 4}, S3 = {1, 4}, and S4 = {2, 5} the set cover could then be S1 and S2. Determine a counterexample for following algorithm on the basis of greedy strategy: Choose the largest subset for cover, and then remove all its elements from universal set. Repeat by adding subset consisting of largest number of uncovered elements until all is covered.
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