2021/05/05 by Agarwal, Pankaj K., Hu, Xiao, Sintos, Stavros +1
#Data Structures and Algorithms (cs.DS) #Databases (cs.DB) #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.2105.01818
This paper considers enumerating answers to similarity-join queries under dynamic updates: Given two sets of n points A,B in ℝd, 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 logO(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 ℓp metric, with logO(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).