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Given a list of sets which contain elements:

[setA: {a, b, e},
 setB: {d, e, c}.
 setC: {a, d}
]

and a list L of elements needed to cover: [x, y, z, ...]

find the smallest list of sets from L whose union contains all elements in the list L.

Is this problem the same as Set-Cover (implying it is NP-Complete)? Or is there something I am missing about this that makes it tractable?

Assume one can determine if an element x exists in a set in constant time.

Iota Tronics
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1 Answers1

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You have two lists. The first is the list of sets L1 whereas the second is the list of elements to cover L2. Discard in polynomial time all the elements that are not in L2 from each set in L1 and you will get a set cover problem. Therefore, if you have a polynomial time algorithm to solve your problem, you will get a polynomial time answer to the Set Cover problem too.

Mahdaoui7
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