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Data summarization is a powerful approach to deal with large-scale data analytics, which has wide applications in web search, recommendation systems, approximate query processing, etc. It computes a small, compact summary that preserves vital properties of the original data. In this paper, we study the data summarization problem of conjunctive query results, i.e., computing a k-size subset of a conjunctive query output, for any given k>0, that optimizes a certain objective. More specifically, we are interested in two commonly studied objectives: cohesion, which measures the maximum distance between a tuple in the query result tuples and its closest tuple in the summary (k-center clustering); and diversity, which measures the pairwise distances between the summary items. A simple approach that computes the entire query output and then applies existing algorithms on top of these materialized tuples suffers from high computational complexity because the query output can be large, e.g., for a relational database of N tuples, the number of result tuples can be NO(1).We propose O(1)-approximation algorithms that compute well-representative summaries of size k in time O(N*kO(1)), or even O(N+ kO(1)) in some cases, without computing all result tuples. We also propose the first efficient (2+\eps)-approximation algorithm for the k-center clustering problem over relational data. Our main idea is to formulate a few oracles that enable us to access specific query result tuples with certain properties, to show how these oracles can be implemented efficiently, and to compute desired summaries with few invocations of these oracles.
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This content will become publicly available on November 4, 2025
Improved Approximation Algorithms for Relational Clustering
Clustering plays a crucial role in computer science, facilitating data analysis and problem-solving across numerous fields. By partitioning large datasets into meaningful groups, clustering reveals hidden structures and relationships within the data, aiding tasks such as unsupervised learning, classification, anomaly detection, and recommendation systems. Particularly in relational databases, where data is distributed across multiple tables, efficient clustering is essential yet challenging due to the computational complexity of joining tables. This paper addresses this challenge by introducing efficient algorithms for k-median and k-means clustering on relational data without the need for pre-computing the join query results. For the relational k-median clustering, we propose the first efficient relative approximation algorithm. For the relational k-means clustering, our algorithm significantly improves both the approximation factor and the running time of the known relational k-means clustering algorithms, which suffer either from large constant approximation factors, or expensive running time. Given a join query q and a database instance D of O(N) tuples, for both k-median and k-means clustering on the results of q on D, we propose randomized (1+ε)γ-approximation algorithms that run in roughly O(k2Nfhw)+T_γ(k2) time, where ε ∈ (0,1) is a constant parameter decided by the user, \fhw is the fractional hyper-tree width of Q, while γ and T_γ(x) represent the approximation factor and the running time, respectively, of a traditional clustering algorithm in the standard computational setting over x points.
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- Award ID(s):
- 2348919
- PAR ID:
- 10618625
- Publisher / Repository:
- ACM (Association for Computing Machinery)
- Date Published:
- Journal Name:
- Proceedings of the ACM on Management of Data
- Volume:
- 2
- Issue:
- 5
- ISSN:
- 2836-6573
- Page Range / eLocation ID:
- 1 to 27
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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