Fundamental Concepts

ALGEBRAIX® technology is unlike any other data management technology on the market today.  The concepts described below provide a foundation for understanding ALGEBRAIX technology and how it uniquely solves the inherent problems of conventional data management.

An Algebra of Data

The underpinning of ALGEBRAIX technology is a hierarchy of three extended set algebras, developed by Algebraix Data Corporation, which extend Boolean algebra to operate on (among other things) ordered pairs (called “couplets” and used to represent attribute-value pairs), sets of couplets (called “extended sets” and used as a mathematical formulation for data records) and sets of extended sets (called “clans” and used as a mathematical formulation for data tables).  These algebras provide full backward compatibility with the relational data model and enable three major technological advances.

A Universal Data Model – The extended set algebras provide a universal means for simultaneously modeling disparate logical and physical data structures and for mathematically mapping any one to any other. This confers a universal data model which enables the simultaneous modeling of multiple disparate logical and physical data structures and mapping them to each other without programming.  As a direct result, the extended set algebras enable:

• Strong data independence, or complete independence of logical data structures from physical data structures;
• Simultaneous management of multiple disparate data models, including flat files (e.g., CSV files), nested hierarchies (e.g., XML documents), relational data tables, directed graphs or any other regular well-defined data structure; and
• Data virtualization, or data access across heterogeneous hardware and software platforms.

A Comprehensive Computing Universe – The extended set algebras provide a means for establishing a comprehensive computing universe comprising all the logical and physical resources within a host system, for which a complete and rigorous mathematical model can be maintained at all times.  As a direct result, the extended set algebras enable:

• Time-stamped nondestructive recording of all data inserts, updates and deletes;
• Establishment of “data immutability” ensuring that all source data enter the computing universe at discrete points in time and is thereafter unchanged until discarded; and
• Establishment of “temporal integrity” in which the value, structure and location of all data are held constant and related over time.

Mathematical Equivalence – In a fundamental departure from all prior data-management technologies, the extended set algebras provide a means for performing all data manipulations via execution of algebraic expressions – i.e., sequences of algebraic operations – and for determining the mathematical equivalence of alternative expressions irrespective of the structures of their operands.  As a direct result, the extended set algebras enable:

• All data manipulations to be performed via mathematical operations;
• Minimization of query-processing operations via
• Substitution of mathematically-optimized sequences of operations for mathematically-equivalent-but-less-efficient sequences of operations;
• Adaptive self-optimizations which exploit mathematical metadata characterizing all working data sets and the relationships between them to minimize data transfers across the persistent-storage/volatile-memory performance barrier and to optimize physical data sets in persistent storage for the fastest possible access based on actual data and query patterns at run-time;
• Data to be distributed across heterogeneous computing networks; and
• Simultaneous in situ discovery, exploration and mining of any combination of locally and globally distributed data via federated peer-to-peer query processing.

The Shortest Path to Results

In addition to providing unequalled data management simplicity and performance, ALGEBRAIX technology offers many other unique features, such as:

• Connect-and-query – because data is independent of any logical or physical structure or application, it does not need to be loaded or modeled.   Simply “connect” the data source (by defining its data structure and location); then run queries.
• Automatic self-tuning – query processing gets faster and faster as more queries are run.
• Real-time update – because data is not loaded, there is no lag between the time data is received or updated and when it can be queried.
• Point-in-time query – temporal integrity enables data to be queried as it existed at any time in its recorded history.

Learn about how ALGEBRAIX technology enables advanced analytics in the Cloud.
For further details about ALGEBRAIX technology, please visit our resource library or contact us.