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  1. Result diversification is extensively studied in the context of search, recommendation, and data exploration. There are numerous algorithms that return top-k results that are both diverse and relevant. These algorithms typically have computational loops that compare the pairwise diversity of records to decide which ones to retain. We propose an access primitive DivGetBatch() that replaces repeated pairwise comparisons of diversity scores of records by pairwise comparisons of “aggregate” diversity scores of a group of records, thereby improving the running time of these algorithms while preserving the same results. We integrate the access primitive inside three representative diversity algorithms and prove that the augmented algorithms leveraging the access primitive preserve original results. We analyze the worst and expected case running times of these algorithms. We propose a computational framework to design this access primitive that has a pre-computed index structure I-tree that is agnostic to the specific details of diversity algorithms. We develop principled solutions to construct and maintain I-tree. Our experiments on multiple large real-world datasets corroborate our theoretical findings, while ensuring up to a 24× speedup. 
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  2. Given m users (voters), where each user casts her preference for a single item (candidate) over n items (candidates) as a ballot, the preference aggregation problem returns k items (candidates) that have the k highest number of preferences (votes). Our work studies this problem considering complex fairness constraints that have to be satisfied via proportionate representations of different values of the group protected attribute(s) in the top- k results. Precisely, we study the margin finding problem under single ballot substitutions , where a single substitution amounts to removing a vote from candidate i and assigning it to candidate j and the goal is to minimize the number of single ballot substitutions needed to guarantee that the top-k results satisfy the fairness constraints. We study several variants of this problem considering how top- k fairness constraints are defined, (i) MFBinaryS and MFMultiS are defined when the fairness (proportionate representation) is defined over a single, binary or multivalued, protected attribute, respectively; (ii) MF-Multi2 is studied when top- k fairness is defined over two different protected attributes; (iii) MFMulti3+ investigates the margin finding problem, considering 3 or more protected attributes. We study these problems theoretically, and present a suite of algorithms with provable guarantees. We conduct rigorous large scale experiments involving multiple real world datasets by appropriately adapting multiple state-of-the-art solutions to demonstrate the effectiveness and scalability of our proposed methods. 
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