Publication Type
Conference Proceeding Article
Version
publishedVersion
Publication Date
6-2021
Abstract
Coresets are succinct summaries of large datasets such that, for a given problem, the solution obtained from a coreset is provably competitive with the solution obtained from the full dataset. As such, coreset-based data summarization techniques have been successfully applied to various problems, e.g., geometric optimization, clustering, and approximate query processing, for scaling them up to massive data. In this paper, we study coresets for the maxima representation of multidimensional data: Given a set �� of points in R �� , where �� is a small constant, and an error parameter �� ∈ (0, 1), a subset �� ⊆ �� is an ��-coreset for the maxima representation of �� iff the maximum of �� is an ��-approximation of the maximum of �� for any vector �� ∈ R �� , where the maximum is taken over the inner products between the set of points (�� or ��) and ��. We define a novel minimum ��-coreset problem that asks for an ��-coreset of the smallest size for the maxima representation of a point set. For the two-dimensional case, we develop an optimal polynomial-time algorithm for the minimum ��-coreset problem by transforming it into the shortest-cycle problem in a directed graph. Then, we prove that this problem is NP-hard in three or higher dimensions and present polynomial-time approximation algorithms in an arbitrary fixed dimension. Finally, we provide extensive experimental results on both real and synthetic datasets to demonstrate the superior performance of our proposed algorithms.
Keywords
Coreset, maxima representation, ��-kernel, convex hull, regret minimizing set
Discipline
Databases and Information Systems | Data Storage Systems
Research Areas
Data Science and Engineering
Publication
Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems (PODS 2021), Virtual Conference, 2021 June 21-23
First Page
138
Last Page
152
Identifier
10.1145/3452021.3458322
Publisher
ACM
City or Country
USA
Citation
1
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.