SearcharxivSearch

arXiv · 2208.02981

Towards Fast Theta-join: A Prefiltering and Amalgamated Partitioning Approach

Abstract

As one of the most useful online processing techniques, the theta-join operation has been utilized by many applications to fully excavate the relationships between data streams in various scenarios. As such, constant research efforts have been put to optimize its performance in the distributed environment, which is typically characterized by reducing the number of Cartesian products as much as possible. In this article, we design and implement a novel fast theta-join algorithm, called Prefap, by developing two distinct techniques - prefiltering and amalgamated partitioning-based on the state-of-the-art FastThetaJoin algorithm to optimize the efficiency of the theta-join operation. Firstly, we develop a prefiltering strategy before data streams are partitioned to reduce the amount of data to be involved and benefit a more fine-grained partitioning. Secondly, to avoid the data streams being partitioned in a coarse-grained isolated manner and improve the quality of the partition-level filtering, we introduce an amalgamated partitioning mechanism that can amalgamate the partitioning boundaries of two data streams to assist a fine-grained partitioning. With the integration of these two techniques into the existing FastThetaJoin algorithm, we design and implement a new framework to achieve a decreased number of Cartesian products and a higher theta-join efficiency. By comparing with existing algorithms, FastThetaJoin in particular, we evaluate the performance of Prefap on both synthetic and real data streams from two-way to multiway theta-join to demonstrate its superiority.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jiashu Wu, Yang Wang, Xiaopeng Fan, Kejiang Ye, Chengzhong Xu. 2022-08-05. Towards Fast Theta-join: A Prefiltering and Amalgamated Partitioning Approach. https://doi.org/10.1002/cpe.6996

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS