Associative Arrays: Unified Mathematics for Spreadsheets, Databases, Matrices, and Graphs

Data processing systems impose multiple views on data as it is processed by the system. These views include spreadsheets, databases, matrices, and graphs. The common theme amongst these views is the need to store and operate on data as whole sets instead of as individual data elements. This work describes a common mathematical representation of these data sets (associative arrays) that applies across a wide range of applications and technologies. Associative arrays unify and simplify these different approaches for representing and manipulating data into common two-dimensional view of data. Specifically, associative arrays (1) reduce the effort required to pass data between steps in a data processing system, (2) allow steps to be interchanged with full confidence that the results will be unchanged, and (3) make it possible to recognize when steps can be simplified or eliminated. Most database system naturally support associative arrays via their tabular interfaces. The D4M implementation of associative arrays uses this feature to provide a common interface across SQL, NoSQL, and NewSQL databases. Keywords-Insider; Big Data; Associative Arrays; Spreadsheets; Database; Matrices; Graphs; Abstract Algebra