K-Regret Queries: From Additive to Multiplicative Utilities

The k-regret queries aim to return a size-k subset of the entire database such that, for any query user that selects a data object in this size-k subset rather than in the entire database, her “regret ratio” is minimized. Here, the regret ratio is modeled by the level of difference in the optimality between the optimal object in the size-k subset returned and the optimal object in the entire database. The optimality of a data object in turn is usually modeled by a utility function of the query user. Compared with traditional top-k queries, the k-regret queries have the advantage of not requiring the users to specify their utility functions. They can discover a size-k subset that minimizes the regret ratio for a whole family of utility functions without knowing any particular of them. Previous studies have answered k-regret queries with additive utility functions such as the linear summation function. However, no existing result has been reported to answer k-regret queries with multiplicative utility functions, which are an important family of utility functions. In this study, we break the barrier of multiplicative utility functions. We present an algorithm that can produce answers with a bounded regret ratio to k-regret queries with multiplicative utility functions. As a case study we apply this algorithm to process a special type of multiplicative utility functions, the Cobb-Douglas function, and a closely related function, the Constant Elasticity of Substitution function. We perform extensive experiments on the proposed algorithm. The results confirm that the proposed algorithm can answer the k-regret queries with multiplicative utility functions efficiently with a constantly low regret ratio.