Abstract: Systems and methods allow the use of algebra to optimize several queries at once by algebraically breaking them into pieces, interleaving them in the most efficient way and then computing the queries together. For instance, a user or application may have many queries to process. A computing device may handle each query sequentially. However, if the computing device handled the queries simultaneously and if they are presented at once, there are ways to algebraically optimize them together by interleaving the tasks required to execute each one and complete the entire batch more efficiently.

Abstract: The systems, methods, devices, and non-transitory media of the various embodiments enable query execution plan graphs to be compared to determine whether all or portions of two or more queries define data sets that are structurally equivalent. Two data sets may be structurally equivalent when each data set may be composed with a bijective relation that yields the other. In the various embodiments, when all or a portion of a first query that has been previously run defines a data set that is structurally equivalent to a data set defined by all or a portion of a second query that is to be run, the structure preserving transform may be applied to the corresponding portion of the second query to transform that portion of the second query into the corresponding portion of the first query, thereby allowing the results from previously running the first query to be reused.