I am looking at the diverse subset problem in Kleinberg and Tardos, shown in the image:
Why can't we give a polynomial time algorithm for this? Cant we iterate through each person a, and then each item i, and then see for each person b $\neq$ a if b has bought item i, then conclude that a and b cannot be diverse? And if we get through all items and no item that a has bought has been bought by b therefore implies they're diverse? Then we do this with each customer. What's wrong with this approach?