Inverse System Matrix Network Path Analysis
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Solution Overview
Problem
Determining characteristics such as connectivity and shortest paths in large networks is computationally intensive and requires significant resources due to the complexity of calculating and managing flow and potential values across numerous vertices and connections.
Innovation Solution
A computer-implemented method using an inverse system matrix to evaluate relative flow and connectivity by building a graph with directional flow and fluidity calculations, applying an offset matrix to ensure linear independence, and identifying the shortest path or connectivity through matrix inversion and relative flow evaluation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional algorithms are used to determine shortest path and connectivity in large networks, then accurate results can be obtained, but computational time and resource requirements increase significantly
Solution Approach 1:
The patent transforms the shortest path problem into an electrical circuit analogy where graph edges become conductors with conductances inversely proportional to edge weights. By solving the resulting linear system of equations using matrix operations, the algorithm achieves O(n³) computational complexity through efficient linear algebra techniques rather than traditional path exploration methods
Solution Approach 2:
The patent replaces traditional mechanical graph traversal algorithms (like Dijkstra's algorithm that systematically explores paths) with an electrical circuit model where potentials and flows naturally determine the shortest path through physical analogies, substituting computational search with mathematical solution of linear equations
2Measurement precision
If traditional algorithms are used to determine shortest path and connectivity in large networks, then accurate results can be obtained, but computational resources increase significantly
Solution Approach 1:
The patent changes the problem parameters by representing the network as an electrical circuit where conductances are inverse of edge weights, transforming the discrete path-finding problem into a continuous system of linear equations that can be solved using optimized matrix operations
Solution Approach 2:
The patent creates a unified mathematical framework using matrix operations that simultaneously solves multiple graph problems including shortest path, connectivity, and flow distribution, allowing a single algorithmic approach to handle various network analysis tasks
3Measurement precision
If complex flow and potential calculations are performed across numerous vertices and connections, then network characteristics can be determined, but the calculation process becomes computationally intensive
Solution Approach 1:
The patent segments the complex network problem into manageable matrix operations by representing vertices as matrix rows/columns and connections as matrix elements, allowing the use of efficient linear algebra algorithms to solve the system in organized stages
Solution Approach 2:
The patent substitutes complex iterative flow and potential calculations with a direct matrix inversion approach, replacing step-by-step numerical simulations with a closed-form mathematical solution that computes all potentials simultaneously
Data Source
AI summary
A computer implemented method for determining a characteristic of a network, the network having a plurality of vertices and a plurality of connections, where at least one of the plurality of vertices is defined as a starting vertex, and at least one of the plurality of vertices is defined as a destination vertex, the method having the steps of: allocating a cost value to each connection, a potential value to the starting vertex and a potential value to the destination vertex, executing an inverse system matrix related to the flow of the network, calculating the relative flow of a connection over all neighboring vertices of each vertex, and determining the characteristic of a network by evaluating the relative flow of each connection.