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Dynamic Enumeration of Similarity Joins

Authors Pankaj K. Agarwal, Xiao Hu, Stavros Sintos, Jun Yang

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Pankaj K. Agarwal
  • Duke University, Durham, NC, USA
Xiao Hu
  • Duke University, Durham, NC, USA
Stavros Sintos
  • University of Chicago, IL, USA
Jun Yang
  • Duke University, Durham, NC, USA

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Pankaj K. Agarwal, Xiao Hu, Stavros Sintos, and Jun Yang. Dynamic Enumeration of Similarity Joins. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 11:1-11:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


This paper considers enumerating answers to similarity-join queries under dynamic updates: Given two sets of n points A,B in ℝ^d, a metric ϕ(⋅), and a distance threshold r > 0, report all pairs of points (a, b) ∈ A × B with ϕ(a,b) ≤ r. Our goal is to store A,B into a dynamic data structure that, whenever asked, can enumerate all result pairs with worst-case delay guarantee, i.e., the time between enumerating two consecutive pairs is bounded. Furthermore, the data structure can be efficiently updated when a point is inserted into or deleted from A or B. We propose several efficient data structures for answering similarity-join queries in low dimension. For exact enumeration of similarity join, we present near-linear-size data structures for 𝓁₁, 𝓁_∞ metrics with log^{O(1)} n update time and delay. We show that such a data structure is not feasible for the 𝓁₂ metric for d ≥ 4. For approximate enumeration of similarity join, where the distance threshold is a soft constraint, we obtain a unified linear-size data structure for 𝓁_p metric, with log^{O(1)} n delay and update time. In high dimensions, we present an efficient data structure with worst-case delay-guarantee using locality sensitive hashing (LSH).

Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures and algorithms for data management
  • dynamic enumeration
  • similarity joins
  • worst-case delay guarantee


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