  The $k$-Maximum Inner Product Search ($k$MIPS) serves as a foundational
component in recommender systems and various data mining tasks. However, while
most existing $k$MIPS approaches prioritize the efficient retrieval of highly
relevant items for users, they often neglect an equally pivotal facet of search
results: \emph{diversity}. To bridge this gap, we revisit and refine the
diversity-aware $k$MIPS (D$k$MIPS) problem by incorporating two well-known
diversity objectives -- minimizing the average and maximum pairwise item
similarities within the results -- into the original relevance objective. This
enhancement, inspired by Maximal Marginal Relevance (MMR), offers users a
controllable trade-off between relevance and diversity. We introduce
\textsc{Greedy} and \textsc{DualGreedy}, two linear scan-based algorithms
tailored for D$k$MIPS. They both achieve data-dependent approximations and,
when aiming to minimize the average pairwise similarity, \textsc{DualGreedy}
attains an approximation ratio of $1/4$ with an additive term for
regularization. To further improve query efficiency, we integrate a lightweight
Ball-Cone Tree (BC-Tree) index with the two algorithms. Finally, comprehensive
experiments on ten real-world data sets demonstrate the efficacy of our
proposed methods, showcasing their capability to efficiently deliver diverse
and relevant search results to users.
