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: Systems, methods, devices, and non-transitory media of the various embodiments enable the query execution graph for insertions, deletions, and streaming queries to be manipulated to maximize a portion of the query execution that is independent of data changes.

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.

Abstract: The systems, methods, devices, and non-transitory media of the various embodiments provide query independent data identification. In various embodiments, query independent data identification may be used to facilitate data reuse. Query independent data identification may be accomplished using an algebraic expression hash (AEH) function to identify data in a graph or table for reuse based on its origin and what has been done to the data. Use of an AEH function may support a top down approach for identification of data reuse and may also facilitate faster searches using an AEH value. For example, a hash-based search of a universe of data sets may facilitate a top down approach to locate the maximal reuse first (as opposed to the last) and may be less sensitive to the size of the universe.

Abstract: Methods and systems for rendering hogels, including notifying one or more rendering nodes that all rendering is complete in response to determining that each of the one or more rendering nodes completes rendering of corresponding one or more subsets of hogel data from 3D data, the rendering nodes being configured to convert the 3D data to the one or more subsets of hogel data.

Abstract: Methods and systems for handling exceptions, including being provided with a catch list, the catch list being a flattened inheritance tree for exception types in ascending inheritance order, receiving an exception from a thread, searching the catch list in ascending inheritance order to find a matching exception type to received exception.

Abstract: Methods and systems for transmitting data, including transmitting a series of packets of data to multiple nodes, each of the multiple nodes being configured to return an acknowledgement of receipt of one or more of the packets of data, and reducing a size of a current packet of data in response to a time to receive an acknowledgment for a previous packet of data being greater than a threshold time.

Abstract: Methods and systems for rendering hogels, including notifying one or more rendering nodes that all rendering is complete in response to determining that each of the one or more rendering nodes completes rendering of corresponding one or more subsets of hogel data from 3D data, the rendering nodes being configured to convert the 3D data to the one or more subsets of hogel data.

Abstract: Methods and systems for rendering hogels, including receiving a set of 3D data at a node, the node comprising a graphics processing unit, storing at least a subset of the set of 3D data in a buffer, rendering a first hogel view from the subset of 3D data using the graphics processing unit, and rendering a second hogel view by accessing the stored subset of 3D data using the graphics processing unit, where the rendering of the second hogel view is performed substantially in series to the rendering of the first hogel view.

Abstract: Methods and systems for rendering hogels, including causing one or more nodes to each load a subset of a hogel data set into a buffer, the one or more nodes being configured to each store the corresponding subset of the hogel data set, distributing a next hogel data set command to the one or more nodes, causing the buffer to be processed in response to the next hogel data set command, and issuing a hogel data set complete command in response to determining that the one or more nodes each return a hogel data subset complete command.