To prove NP, show an outline (pseudo-code okay) of the certifier algorithm and show that

(a) its running time is polynomial

(b) the token (i.e., certificate) size is bounded by a polynomial function of the Diverse-Set problem instance size.

To prove NP-hard, it would be easier to pick Independent-Set and reduce it to Diverse-Set. For this, provide the specific reduction mechanism and then show that (a) the reduction take polynomial time and (b) the Independent-Set problem instance has an independent set of size at most k if and only if the reduced Diverse-Set problem instance has a diverse set of size at most k.

Astore trying to analyze the behavior ofits customers will often maintain a two-dimensional array A, where the rows correspond to its customers and the to the it sells. entry Ali, jl specifies the quantity of product j that has been purchased by customer i. Here's a tiny example of such an array A. liquid detergent beer diapers cat litter Raj Alanis 2 Chelsea 0 One thing that a store might want to do with this data is thefollowing. Let us say that a subset s of the customers is diverse if no two of the product, at most one of the customer in s has ever bought it). A diverse set of customers can be useful, for example, as a target pool for market research. We can now define the Diverse Subset Problem as follows: Given an m x n array A as defined above, and a number k m, is there a subset of at least k of customers that is diverse? Show that Diverse Subset is NP-complete