Ignorant vs. Anonymous Recommendations

We start with an unknown binary n x m matrix, where the entries correspond to the preferences of n users on m items. The goal is to find at least one item per user that the user likes, with as few queries as possible. Since there are matrices where any algorithm performs badly without any preliminary knowledge of the input matrix, we reveal an anonymized version of the input matrix to the algorithm in the beginning of the execution. The input matrix is anonymized by shuffling the rows according to a randomly chosen hidden permutation. We observe that this anonymous recommendation problem can be seen as an adaptive variant of the Min Sum Set Cover problem and show that the greedy solution for the original version of the problem provides a constant approximation for the adaptive version.