Tree Sub-Graph Distance Approximation in Large Graphs
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Solution Overview
Problem
Existing methods for extracting information from large graphical models are computationally intensive, requiring significant time and effort to determine shortest distances between nodes, especially in graphs with thousands or millions of interconnected nodes.
Innovation Solution
The system constructs tree sub-graphs based on hyperbolic properties of the graph, selecting root nodes using various criteria such as distance and degree, and expanding levels in descending order of node degrees to estimate shortest distances efficiently.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional methods are used to extract information from large graphical models, then comprehensive information can be obtained, but computational time and effort increase significantly
Solution Approach 1:
The patent divides the large graph into multiple tree sub-graphs, each rooted at a different node. By segmenting the graph into these hierarchical tree structures, the system can estimate distances more efficiently without examining the entire graph, thus reducing computational time while maintaining accuracy.
Solution Approach 2:
The patent performs preliminary actions by constructing tree sub-graphs in advance and organizing nodes into hierarchical levels based on their distances from root nodes. This pre-computation allows for rapid distance estimation queries later, as the structural work has already been completed.
2Measurement precision
If the graph is fully explored to ensure accurate distance measurement, then precision is maintained, but computational complexity increases
Solution Approach 1:
The graph is segmented into multiple tree sub-graphs, each providing a different perspective on the distance relationships. By combining results from multiple segmented views, the system achieves accurate distance measurement without the complexity of exploring the entire graph structure in detail.
Solution Approach 2:
The patent uses multiple tree sub-graphs (excessive action) to estimate distances, where each tree provides a partial view of the graph. By taking the minimum distance across multiple trees, the system achieves accurate results without requiring a complete and exhaustive analysis of all possible paths.
3Measurement precision
If more root nodes are selected to improve distance estimation accuracy, then measurement precision increases, but the number of tree sub-graphs and computational effort increases
Solution Approach 1:
The patent employs a moderate number of root nodes (excessive but not excessive) to construct tree sub-graphs. This provides sufficient accuracy for distance estimation without overwhelming the system with too many trees. The patent balances the number of root nodes to achieve good accuracy while maintaining reasonable processing efficiency.
Data Source
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AI summary
Systems and methods are provided for constructing a collection of one or more tree sub-graph representations of a graph including multiple interconnected nodes, where the one or more tree sub-graph representations of the graph are used to estimate the shortest distance between any two nodes of a graph. One of the features of the systems and methods disclosed herein is a methodology for the selection or designation of root nodes for constructing the collection of the one or more tree sub-graph representations. Another feature of the present disclosure is a methodology of expanding the parent nodes in a given level of the tree sub-graph representations into one or more child nodes in a successive level of the tree-graph representations based on a descending order of degree of the parent nodes.