ProPolyne Wavelet Algorithm for Polynomial Range-Sum Query Evaluation
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Solution Overview
Problem
Existing methods for evaluating range aggregate queries in database systems are inefficient due to high I/O and computational overhead, and cannot effectively control structural error, especially when dealing with higher order polynomials and batches of queries.
Innovation Solution
The use of a wavelet-based algorithm, ProPolyne, which transforms queries into a compressed form to produce progressive and exact results by filtering queries until a moment condition is met, allowing for efficient range-sum queries in a database with reduced storage and computational costs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If existing OLAP techniques are used to support polynomial range-sums by treating each monomial as a separate measure, then query evaluation capability is improved, but storage and maintenance cost increases significantly
Solution Approach 1:
The patent applies universality by creating a single data cube structure that can evaluate multiple polynomial range-sum queries of different degrees simultaneously. Instead of building separate data cubes for each monomial, the system uses one unified cube that handles queries of varying polynomial degrees, reducing storage requirements while maintaining versatile query evaluation capability.
2Measurement precision
If exact algorithms are used for range aggregate query evaluation, then measurement precision is improved, but computational overhead increases
Solution Approach 1:
The patent applies preliminary action by pre-computing and storing aggregate values in a data cube structure before queries are executed. The cube is built in advance with all necessary aggregate information, allowing queries to be answered quickly by simply retrieving pre-computed values rather than calculating them at query time, thus achieving both exact results and high speed.
Solution Approach 2:
The patent applies dynamics by implementing a progressive evaluation mechanism that can adapt to different query requirements. The system can dynamically adjust the level of detail returned, providing approximate results for quick insights or exact results when needed, and can handle batches of queries by sharing computational work across them.
3Productivity
If approximate techniques are used to minimize single query error, then query evaluation speed is improved, but structural error in the result set cannot be controlled
Solution Approach 1:
The patent applies feedback by implementing a progressive evaluation approach that provides intermediate results with associated error bounds. As the evaluation progresses, the system refines the results and tightens the error bounds, allowing users to stop at any point with a guaranteed error margin. This feedback mechanism ensures both speed (by allowing early termination) and reliability (by controlling structural error through progressive refinement).
Data Source
AI summary
Provided are methods, computer programs and systems that optimize database queries using a wavelet transform of the query. Also provided are methods and systems for optimal disk placement for wavelet data.