Question: Find a constant ratio approximation algorithm. Let us have a set of clauses of type (x or y or z) which always contain a disjunction

Find a constant ratio approximation algorithm. Let us have a set of clauses of type (x or y or z) which always contain a disjunction of at most three variables and never contain negation. Next, let's have a function that assigns an integer weight to each variable. The aim is to find a subset of variables with the smallest possible sum of weights such that that setting these variables to 1 will fulfill all clauses. This problem is NP-complete, but there is an approximation algorithm with a constant approximation ratio. Find such an algorithm and prove that it has the required properties. The approximation ratio will be just 3.

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