The Branch-and-Bound Ranked Search algorithm (BRS) is an efficient method for answering top-k queries based on R-trees using multivariate scoring functions. To make BRS effective with ascending rankings, the algorithm must be able to identify lower bounds of the scoring functions for exploring search partitions. This paper presents BRS supporting parabolic polynomials. These functions are common to minimize combined scores over different attributes and cover a variety of applications. To the best of our knowledge the problem to develop an algorithm for computing lower bounds for the BRS method has not been well addressed yet
