Network Path Generation via Linear System Resolution
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Solution Overview
Problem
Existing methods for generating alternative network paths, such as the plateau method and penalty method, often produce routes that lack robustness and are computationally expensive, making them impractical for real-time applications.
Innovation Solution
The proposed solution involves using a computer-implemented method that generates alternative paths by resolving a linear system of weights over a reduced network graph, propagating solutions through partitions, and employing interpolation transforms to recover flows, thereby identifying robust and efficient routes across the network.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing methods (plateau method, penalty method) are used to generate alternative network paths, then alternative routes can be obtained, but the generated routes lack robustness and the computational cost is high
Solution Approach 1:
The network graph is partitioned into multiple subgraphs, and each subgraph is further reduced to a reduced subgraph containing only boundary nodes. This segmentation allows the linear system to be resolved over smaller, manageable subgraphs rather than the entire network, reducing computational complexity while maintaining robustness through the preservation of boundary node connections that represent critical routing options.
Solution Approach 2:
Internal nodes of each subgraph are extracted and eliminated to form reduced subgraphs containing only boundary nodes. This extraction process reduces the size of the linear system that needs to be solved, improving computational efficiency. The boundary nodes are retained as they represent the essential connection points for alternative path generation.
2Reliability
If existing methods are used to generate alternative paths, then routes can be provided for fault tolerance, but the methods are computationally expensive and impractical for real-time applications
Solution Approach 1:
The network graph is pre-partitioned into subgraphs and reduced to reduced subgraphs before the actual path generation query is processed. The interpolation transforms are pre-computed based on the reduced subgraphs. This preliminary action ensures that when a path generation query arrives, the system can quickly resolve the linear system over the already-reduced subgraphs and apply the pre-computed interpolation transforms, significantly reducing computation time while maintaining fault tolerance through the robust alternative path generation.
3Measurement precision
If the network graph is processed in full detail, then accurate flows can be determined, but the computational resources required are excessive for resource-constrained devices
Solution Approach 1:
Different parts of the network graph are treated differently: boundary nodes are retained in full detail in the reduced subgraphs to maintain accuracy for flow determination at critical connection points, while internal nodes are eliminated to reduce computational complexity. The interpolation transforms are specifically designed to recover accurate flows at boundary nodes based on the reduced subgraph solutions, ensuring measurement precision where it matters most while reducing device complexity requirements.
Data Source
AI summary
Example aspects of the present disclosure provide for an example computer-implemented method for generating alternative network paths, the example method including obtaining a network graph; determining flows respectively for edges of the network graph by: resolving a linear system of weights associated with the edges, the linear system resolved over a reduced network graph, and propagating a solution of the linear system into a respective partition of a plurality of partitions of the network graph to determine at least one of the flows within the respective partition; and determining a plurality of alternative paths across the network graph.