Name
Abstract | ||
|---|---|---|
This paper considers enumerating answers to similarity-join queries under dynamic updates: Given two sets of $n$ points $A,B$ in $\mathbb{R}^d$, a metric $\phi(\cdot)$, and a distance threshold $r > 0$, report all pairs of points $(a, b) \in A \times B$ with $\phi(a,b) \le r$. 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 $\ell_1, \ell_\infty$ metrics with $\log^{O(1)} n$ update time and delay. We show that such a data structure is not feasible for the $\ell_2$ metric for $d \ge 4$. For approximate enumeration of similarity join, where the distance threshold is a soft constraint, we obtain a unified linear-size data structure for $\ell_p$ 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). |
Year | DOI | Venue |
|---|---|---|
2021 | 10.4230/LIPIcs.ICALP.2021.11 | ICALP |
DocType | Citations | PageRank |
Conference | 0 | 0.34 |
References | Authors | |
0 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Pankaj K. Agarwal | 1 | 5257 | 593.81 |
| Xiao Hu | 2 | 13 | 8.91 |
| Stavros Sintos | 3 | 0 | 0.34 |
| Jun Yang | 4 | 2762 | 241.66 |