Difference Matrix Compression for Combinatorial Optimization
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Solution Overview
Problem
The high communication cost and data volume associated with transmitting large matrices for combinatorial optimization problems become a bottleneck when solving the same type of problem repeatedly, as the entire matrix needs to be transmitted each time, leading to inefficient data transfer and processing.
Innovation Solution
A system that calculates a difference matrix between the previous and latest matrices, compresses this difference matrix, and transmits it to a solution device, which then restores and uses it to derive the latest matrix and find the solution, reducing the need for full matrix transmission.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the entire matrix is transmitted each time to solve combinatorial optimization problems repeatedly, then the solution device can obtain the latest problem data, but the communication volume and data transfer time increase significantly
Solution Approach 1:
The patent extracts only the changed elements (difference matrix) from the complete problem matrix and transmits them separately from the unchanged base matrix. This allows the solution device to reconstruct the latest problem matrix by combining the base matrix with the difference matrix, significantly reducing communication volume while maintaining complete and accurate problem data.
Solution Approach 2:
The problem matrix is segmented into two parts: a base matrix containing unchanged elements and a difference matrix containing only the changed elements. This segmentation allows selective transmission of only the necessary updates rather than the entire matrix, reducing communication overhead while ensuring data completeness.
2Reliability
If the entire matrix is transmitted each time, then the latest problem data is available at the solution device, but the communication cost and data volume become a bottleneck
Solution Approach 1:
The patent extracts only the changed elements (difference matrix) from the complete problem matrix and transmits them separately from the unchanged base matrix. This allows the solution device to reconstruct the latest problem matrix by combining the base matrix with the difference matrix, significantly reducing communication volume while maintaining complete and accurate problem data.
Solution Approach 2:
Instead of transmitting the complete matrix (excessive action), the patent transmits only the necessary portion (difference matrix) that contains the changes. This partial transmission approach reduces communication cost and energy consumption while still providing the solution device with all necessary information to solve the latest problem.
3Loss of time
If the difference matrix is compressed using sparse matrix methods, then the communication volume is reduced, but additional processing steps are required for compression and restoration
Solution Approach 1:
The patent changes the representation parameters of the difference matrix by applying sparse matrix compression techniques (such as CSR or COO formats). This transforms the matrix from a dense format to a sparse format that stores only non-zero elements, significantly reducing the data volume for transmission while enabling efficient storage and processing at the receiving end.
Data Source
AI summary
The difference matrix calculation means 72 calculates a difference matrix which is a difference between a first matrix representing a combinatorial optimization problem for which a solution was found last time and a second matrix representing the latest combinatorial optimization problem. The difference matrix compression means 73 compresses the difference matrix. The transmission means 74 transmits the difference matrix after compression to a combinatorial optimization problem solution device that finds a solution to the combinatorial optimization problem.