Sparse Key Matrix Encoding to Avoid Two-Core Cycles
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Sparse linear systems used for encoding key-value pairs in key-value databases result in two-core cycles, increasing computation complexity and inefficiency in encoding and decoding processes.
Innovation Solution
Generate a random binary matrix of at least weight-three, assign keys to rows, append a dense binary matrix, and process the key matrix to output an encoding vector, using an approximate lower triangular matrix to reduce computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of substance
If sparse linear systems are used for encoding key-value pairs, then the encoding compactness is improved, but the computation complexity increases due to two-core cycles
Solution Approach 1:
The patent changes the structural parameters of the key matrix by enforcing a minimum weight of three for each row and using approximate lower triangular matrix factorization. This parameter change eliminates two-core cycles while maintaining the sparse structure needed for compact encoding, thus resolving the contradiction between encoding compactness and computation complexity
Solution Approach 2:
The patent extracts and eliminates the problematic two-core cycle structures from the key matrix by using minimum weight-three constraints and approximate lower triangular factorization. This removal of harmful structural elements reduces computation complexity while preserving the essential sparse encoding properties
2Productivity
If sparse linear systems are used for encoding key-value pairs, then the encoding rate is improved, but the decoding time increases due to computational complexity
Solution Approach 1:
The patent performs preliminary action by pre-factorizing the key matrix into approximate lower triangular form during the encoding phase. This preliminary factorization enables faster decoding operations later, as the structured factorization results can be reused, thus improving decoding speed without sacrificing encoding rate
Solution Approach 2:
By changing the matrix structure to minimum weight-three with approximate lower triangular properties, the patent optimizes both encoding and decoding performance. The structured parameter changes enable efficient algorithms for both operations, improving encoding rate while reducing decoding time compared to general sparse systems
3Productivity
If a random binary matrix is used, then the encoding efficiency is improved, but the reliability decreases due to potential two-core cycles
Solution Approach 1:
The patent changes the parameter constraints of the random binary matrix by enforcing a minimum weight of three for each row. This parameter change maintains the randomness needed for encoding efficiency while eliminating two-core cycles, thus improving encoding reliability without sacrificing efficiency
Solution Approach 2:
The patent converts the potential harm of two-core cycles into a benefit by using minimum weight-three constraints. The increased weight requirement, while seemingly adding complexity, actually eliminates problematic two-core structures and improves matrix reliability, turning a potential defect into a protective feature
Data Source
AI summary
A method is disclosed. The method comprises a receiving a plurality of key-value pairs. The method then generates a random binary matrix of at least weight three. The random binary matrix has a number of non-zero binary values equal to the weight in each row. The method can then assign each key in the plurality of key-value pairs to a row in the random binary matrix. A key matrix can then be generated by appending a dense binary matrix to the random binary matrix. The method can then process the key matrix to output an encoding vector that encodes the values of the plurality of key-value pairs.