Question: The Integer Knapsack problem is defined as follows: INTEGER KNAPSACK Given a set of n items S, each with a weight, wi, and a

The Integer Knapsack problem is defined as follows: INTEGER KNAPSACK Given a set of n items S, each with a weight, wi, and a value, vi, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit, W, and the total value is as large as possible. (a) Provide a polynomial-time approximation algorithm for this problem with approximation ratio and analyze its complexity. You do not need to provide pseudocode for this, just include enoguh detail that the complexity is clearly shown. (b) Establish tight bounds on the approximation ratio for your algorithm. i.e. Prove that a ratio of is always guaranteed, and give an example input for which the algorithm fail to do better than that.

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