
The PGMindex: a multicriteria, compressed and learned approach to data indexing
The recent introduction of learned indexes has shaken the foundations of...
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Nearly Optimal Static Las Vegas Succinct Dictionary
Given a set S of n (distinct) keys from key space [U], each associated w...
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FaultTolerant AllPairs Mincuts
Let G=(V,E) be an undirected unweighted graph on n vertices and m edges....
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Leveraging Soft Functional Dependencies for Indexing Multidimensional Data
A new proposal in database indexing has been for index structures to aut...
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Kernel Density Estimation through Density Constrained Near Neighbor Search
In this paper we revisit the kernel density estimation problem: given a ...
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The Price of Tailoring the Index to Your Data: Poisoning Attacks on Learned Index Structures
The concept of learned index structures relies on the idea that the inpu...
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Computing Shapley Values for Mean Width in 3D
The Shapley value is a common tool in game theory to evaluate the import...
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Superseding traditional indexes by orchestrating learning and geometry
We design the first learned index that solves the dictionary problem with time and space complexity provably better than classic data structures for hierarchical memories, such as Btrees, and modern learned indexes. We call our solution the Piecewise Geometric Model index (PGMindex) because it turns the indexing of a sequence of keys into the coverage of a sequence of 2Dpoints via linear models (i.e. segments) suitably learned to trade query time vs space efficiency. This idea comes from some known heuristic results which we strengthen by showing that the minimal number of such segments can be computed via known and optimal streaming algorithms. Our index is then obtained by recursively applying this geometric idea that guarantees a smoothed adaptation to the "geometric complexity" of the input data. Finally, we propose a variant of the index that adapts not only to the distribution of the dictionary keys but also to their access frequencies, thus obtaining the first distributionaware learned index. The second main contribution of this paper is the proposal and study of the concept of Multicriteria Data Structure, namely one that asks a data structure to adapt in an automatic way to the constraints imposed by the application of use. We show that our index is a multicriteria data structure because its significant flexibility in storage and query time can be exploited by a properly designed optimisation algorithm that efficiently finds its best design setting in order to match the input constraints. A thorough experimental analysis shows that our index and its multicriteria variant improve uniformly, over both time and space, classic and learned indexes up to several orders of magnitude.
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