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F-IVM: Analytics over Relational Databases under Updates
This article describes F-IVM, a unified approach for maintaining analytics
over changing relational data. We exemplify its versatility in four
disciplines: processing queries with group-by aggregates and joins; learning
linear regression models using the covariance matrix of the input features;
building Chow-Liu trees using pairwise mutual information of the input
features; and matrix chain multiplication.
F-IVM has three main ingredients: higher-order incremental view maintenance;
factorized computation; and ring abstraction. F-IVM reduces the maintenance of
a task to that of a hierarchy of simple views. Such views are functions mapping
keys, which are tuples of input values, to payloads, which are elements from a
ring. F-IVM also supports efficient factorized computation over keys, payloads,
and updates. Finally, F-IVM treats uniformly seemingly disparate tasks. In the
key space, all tasks require joins and variable marginalization. In the payload
space, tasks differ in the definition of the sum and product ring operations.
We implemented F-IVM on top of DBToaster and show that it can outperform
classical first-order and fully recursive higher-order incremental view
maintenance by orders of magnitude while using less memory