Suppose a hotel reservation scenario, given $ m $ classified lists of attribute values such as distance, price, amenities (normalized between $ 0 $ and $ 1 $), and a unifying linear score function $ F ( cdot) = alpha_1 * score_1 + alpha_2 * score_2 + alpha_3 * score_3 $, the threshold algorithm (TA) is optimal for finding$ k $ results that have more $ F $ values.
However, consider a paging scenario with a page index $ p $ and page size $ k $. Indeed, instead of asking for$ k $ which can be obtained from the indices (0, k) in the final classified list, we ask (pk, (p + 1) k). What is the best solution to get this results window?
You can think of this as paging the merged results to a unified scoring function when there are multiple data sources that each contain a score value, but the merged results have a combined score value as a function ( linear) of individual score values.
Completely naive: taking into account the multiple classified results, calculate the unified score, sort them, cut them according to your needs.
Potentially better but ineffective when requesting lower ranking results (pages later):
Run the threshold algorithm and ask for top- (p + 1) k, return it (pk, (p + 1) k).