Generic Techniques for Building Top-k Structures

Rahul, S and Tao, Y (2022) Generic Techniques for Building Top-k Structures. In: ACM Transactions on Algorithms, 18 (4).

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Abstract

A reporting query returns the objects satisfying a predicate q from an input set. In prioritized reporting, each object carries a real-valued weight (which can be query dependent), and a query returns the objects that satisfy q and have weights at least a threshold τ. A top-k query finds, among all the objects satisfying q, the k ones of the largest weights; a max query is a special instance with k = 1. We want to design data structures of small space to support queries (and possibly updates) efficiently.Previous work has shown that a top-k structure can also support max and prioritized queries with no performance deterioration. This article explores the opposite direction: do prioritized queries, possibly combined with max queries, imply top-k search? Subject to mild conditions, we provide affirmative answers with two reduction techniques. The first converts a prioritized structure into a static top-k structure with the same space complexity and only a logarithmic blowup in query time. If a max structure is available in addition, our second reduction yields a top-k structure with no degradation in expected performance (this holds for the space, query, and update complexities). Our techniques significantly simplify the design of top-k structures because structures for max and prioritized queries are often easier to obtain. We demonstrate this by developing top-k structures for interval stabbing, 3D dominance, halfspace reporting, linear ranking, and L∞ nearest neighbor search in the RAM and the external memory computation models.

Item Type:	Journal Article
Publication:	ACM Transactions on Algorithms
Publisher:	Association for Computing Machinery
Additional Information:	The copyright for this article belongs to the Association for Computing Machinery.
Keywords:	Data structures; Deterioration; Random access storage; Structural design, reductions; Condition; Design data; Input set; Max-query; Performance deterioration; Reduction techniques; Space complexity; Top-k; Top-k query, Nearest neighbor search
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	15 Jul 2023 07:11
Last Modified:	15 Jul 2023 07:11
URI:	https://eprints.iisc.ac.in/id/eprint/82483

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