In this paper, we initiate a theoretical study of what we call the join covering problem. We are given a natural join query instance $Q$ on $n$ attributes and $m$ relations $(R_i)_{i \in [m]}$. Let $J_{Q} = \ \Join_{i=1}^m R_i$ denote the join output of $Q$. In addition to $Q$, we are given a parameter $Δ: 1\le Δ\le n$ and our goal is to compute the smallest subset $\mathcal{T}_{Q, Δ} \subseteq J_{Q}$ such that every tuple in $J_{Q}$ is within Hamming distance $Δ- 1$ from some tuple in $\mathcal{T}_{Q, Δ}$. The join covering problem captures both computing the natural join from database theory and constructing a covering code with covering radius $Δ- 1$ from coding theory, as special cases.
We consider the combinatorial version of the join covering problem, where our goal is to determine the worst-case $|\mathcal{T}_{Q, Δ}|$ in terms of the structure of $Q$ and value of $Δ$. One obvious approach to upper bound $|\mathcal{T}_{Q, Δ}|$ is to exploit a distance property (of Hamming distance) from coding theory and combine it with the worst-case bounds on output size of natural joins (AGM bound hereon) due to Atserias, Grohe and Marx [SIAM J. of Computing'13]. Somewhat surprisingly, this approach is not tight even for the case when the input relations have arity at most two. Instead, we show that using the polymatroid degree-based bound of Abo Khamis, Ngo and Suciu [PODS'17] in place of the AGM bound gives us a tight bound (up to constant factors) on the $|\mathcal{T}_{Q, Δ}|$ for the arity two case. We prove lower bounds for $|\mathcal{T}_{Q, Δ}|$ using well-known classes of error-correcting codes e.g, Reed-Solomon codes. We can extend our results for the arity two case to general arity with a polynomial gap between our upper and lower bounds.
Graph pattern matching (e.g., finding all cycles and cliques) has become an important component in many critical domains such as social networks, biology, and cyber-security. This development motivated research to develop faster algorithms that target graph pattern matching. In recent years, the database community has shown that mapping graph pattern matching problems to a new class of relational join algorithms provides an efficient framework for computing these problems. In this paper, we argue that this new class of relational join algorithms is highly amenable to specialized hardware accel…
带有捕获变量的正则表达式，也称为“regex公式”，从文本中提取跨度（间隔位置）的关系。这些关系可以通过关系代数进一步操纵，如在文档speeding的上下文中所研究的，Fagin et al.的信息抽取的形式框架。我们调查的复杂性查询文本的合取词（CQ）和联盟的CQ（UCQ）的顶部正则表达式公式。我们证明了关系世界的下界（NP-完全性和W[1]-硬度）在我们的设置中也成立;特别是，硬度已经达到了单字符文本！然而，关系世界的上限并没有延续。与关系世界不同，非循环CQ，甚至是伽马非循环CQ都很难计算。困难的根源在于，实例化由正则表达式公式定义的关系可能很难，仅仅因为它具有指数数量的元组。然而，我们能够建立一般的上限。特别是，UCQ可以用多项式延迟来计算，只要每个CQ都有有限数量的原子（而联合和投影可以是任意的）。此外，当参数为UCQ的大小时，UCQ评估可通过FPT（Fixed-Parameter Tractable）延迟来求解。
Joins in native graph database management systems (GDBMSs) are predefined to the system as edges, which are indexed in adjacency list indices and serve as pointers. This contrasts with and can be more performant than value-based joins in RDBMSs and has lead researchers to investigate ways to integrate predefined joins directly into RDBMSs. Existing approaches adopt a strict separation of graph and relational data and processors, where a graph-specific processor uses left-deep and index nested loop joins for a subset of joins. This may be suboptimal, and may lead to non-sequential scans of data…
A closer integration of machine learning and relational databases has gained steam in recent years due to the fact that the training data to many ML tasks is the results of a relational query (most often, a join-select query). In a federated setting, this poses an additional challenge, that the tables are held by different parties as their private data, and the parties would like to train the model without having to use a trusted third party. Existing work has only considered the case where the training data is stored in a flat table that has been vertically partitioned, which corresponds to a…
We investigate the complexity of evaluating queries in Relational Algebra (RA) over the relations extracted by regex formulas (i.e., regular expressions with capture variables) over text documents. Such queries, also known as the regular document spanners, were shown to have an evaluation with polynomial delay for every positive RA expression (i.e., consisting of only natural joins, projections and unions); here, the RA expression is fixed and the input consists of both the regex formulas and the document. In this work, we explore the implication of two fundamental generalizations. The first i…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
We propose unifying techniques from probabilistic databases and relational embedding models with the goal of performing complex queries on incomplete and uncertain data. We formalize a probabilistic database model with respect to which all queries are done. This allows us to leverage the rich literature of theory and algorithms from probabilistic databases for solving problems. While this formalization can be used with any relational embedding model, the lack of a well-defined joint probability distribution causes simple query problems to become provably hard. With this in mind, we introduce \…
TablePuppet: A Generic Framework for Relational Federated Learning
ETH Zürich（苏黎世联邦理工学院）；UIUC（伊利诺伊大学厄巴纳-香槟分校）；Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）；University of Chicago（芝加哥大学）；Tsinghua University（清华大学）；Microsoft Research（微软研究院）
