Target-Based Shortest Path Extraction Using Tree Graphs
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Solution Overview
Problem
The existing methods for calculating the shortest distance between multiple sites become impractically complex as the number of sites increases, making it difficult to extract the shortest path due to an astronomical number of cases, which is virtually impossible to calculate efficiently.
Innovation Solution
A target-based shortest path extracting method and device that recognizes three or more sites within a designated area, sets a start site, and uses a tree graph to connect sites, employing algorithms to extract the shortest path by minimizing unnecessary site searching, such as the Minimum Spanning Tree (MST) and connecting tree lines based on site indices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If all distances between sites are calculated to extract the shortest path, then the shortest path can be found, but the calculation complexity increases astronomically with the number of sites
Solution Approach 1:
The patent segments the complete graph into a tree graph structure by selecting a root site and establishing hierarchical parent-child relationships. This segmentation reduces the problem from calculating all pairwise distances to calculating distances only along tree paths from the root to each site, transforming the astronomical complexity into polynomial complexity.
Solution Approach 2:
The patent extracts only the necessary path information from the complete graph by building a minimum spanning tree. Instead of considering all possible paths between all site pairs, it extracts and retains only the edges that form the shortest path tree from the root site, discarding redundant edges that do not contribute to the shortest path calculation.
2Measurement precision
If all sites are searched to ensure the shortest path is found, then the shortest path can be extracted, but the path searching time increases significantly
Solution Approach 1:
The patent performs preliminary action by pre-establishing the tree graph structure and calculating distances from the root site to all other sites along tree paths before the actual shortest path query. This preliminary setup creates a hierarchical framework that enables efficient path extraction without requiring exhaustive search during the query phase.
Solution Approach 2:
The patent extracts and utilizes only the essential distance information along tree paths, ignoring distances and paths that do not contribute to the shortest path from the root. This selective extraction of necessary information reduces the search space and computation time while maintaining accuracy.
3Adaptability or versatility
If the number of sites increases, then more sites can be processed, but the number of cases to calculate increases to an astronomical number
Solution Approach 1:
The patent applies segmentation by organizing sites into a hierarchical tree structure where each site (except the root) has exactly one parent. This segmentation reduces the number of calculation cases from O(n²) pairwise comparisons to O(n) path calculations from the root, allowing the system to handle a large number of sites efficiently.
Solution Approach 2:
The patent transitions from considering all possible paths between any two sites (complete graph approach) to considering only paths from the root site to other sites (tree graph approach). This dimensional reduction in the search space transforms the problem from exponential complexity to polynomial complexity, enabling processing of large numbers of sites.
Data Source
AI summary
There is provided a target-based shortest path extracting method. The method includes recognizing three or more sites within a designated area of a target and setting a start site among the recognized sites; extracting a tree graph by connecting sites within the designated area, starting with the start site; and extracting the shortest path between sites within the designated area of the target by connecting tree lines of the tree graph, starting with the start site.