Unformatted text preview: floppy disks. (a) Define a corresponding decision problem to this problem. (b) Design an NPalgorithm for this decision problem. (c) Prove that this problem is NPhard. 3 The minimum set cover problem is defined as follows. Let S 1 , S 2 , S 3 , …, S n be n sets. The union U of the n sets is the set of all elements that occur in these sets. Now, we wish to find the minimum number of sets among the n sets that contain all elements in U. For example, S 1 = { a , b }, S 1 = { b , c }, S 3 = { a , c }, U = S 1 ∪ S 2 ∪ S 3 = { a , b , c }. Since S 1 ∪ S 2 = { a , b , c }= U, and no single set contains all elements, S 1 and S 2 is a minimum set cover. (a) Redefine the minimum set cover problem as a decision problem. (b) Prove that the minimum set cover problem is NPhard. 1...
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 Winter '05
 Shen
 Algorithms, Computational complexity theory, Natural number, decision problem, SET COVER problem

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