Matrix Data System for O(log n) Function Computation
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Solution Overview
Problem
Current databases are inefficient in performing complex mathematical calculations on large, rapidly updated data sets, particularly in distributed systems, as they often rely on O(n) speed operations for functions like finding the maximum or average value, which can be slow and resource-intensive.
Innovation Solution
The matrix data system employs descriptive vectors to cache intermediate results of mathematical calculations, allowing for O(log n) speed operations by storing and reusing partial function solutions in a tree hierarchy, and optionally using sampling for quick estimates with confidence intervals.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If traditional database operations (O(n)) are used for mathematical calculations on large data sets, then accuracy is maintained, but computation speed deteriorates
Solution Approach 1:
The system performs preliminary calculations by maintaining descriptive vectors that cache intermediate results of mathematical functions (max, min, sum, average, etc.) as data is inserted or updated. When a query is requested, the system retrieves pre-computed descriptive vectors and combines them to produce the final result, avoiding the need to scan all n records at query time. This transforms O(n) query operations into O(1) or O(log n) operations by having performed the computational work in advance during data modification operations.
2Speed
If all intermediate calculation results are cached to achieve O(1) speed, then computation speed improves, but memory usage increases
Solution Approach 1:
The system maintains descriptive vectors with different levels of detail and granularity for different data ranges and functions. Rather than uniformly caching all possible intermediate results, the system stores descriptive vectors selectively based on the specific query requirements, data distribution characteristics, and resource availability. The descriptive vectors capture essential statistical properties (min, max, sum, count, and custom functions) locally for specific data partitions, enabling efficient query resolution without requiring complete pre-computation of all possible aggregate results.
3Measurement precision
If descriptive vectors are maintained for all mathematical functions, then computation accuracy is preserved, but system complexity increases
Solution Approach 1:
The system implements a universal descriptive vector structure that can represent and compute multiple mathematical functions (maximum, minimum, sum, average, and user-defined functions) using a common framework. The descriptive vector maintains a set of statistical properties and function values that can be combined through algebraic operations to derive results for various aggregate functions. This multi-functional approach allows the system to compute different types of aggregate queries by combining the same underlying descriptive vector data, reducing the need for separate complex data structures for each function type.
Data Source
AI summary
A matrix data system enabling efficient function computation on source vector data by an array of matrix data servers is disclosed. Descriptive vectors, that describe partial function solutions on underlying source vector data, are computed and stored by the array of matrix data servers and utilized to efficiently compute function solutions. An array of matrix data servers can operate as a single entity, with function computation distributed across the servers in the array. The system can cache computed descriptive vectors, only pulling source vector data as necessary. The system can produce solutions in matrix, tabular, vector or graphical form. In addition to computing solutions, the system can trigger processing on data events, such as when a function or value relating to source vector data changes or goes out of a bounded range. The system is also capable predicting future events based on historical data.