Shortest Path Identification Using Edge and Path Tables
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Solution Overview
Problem
Finding shortest paths in complex graphs can be computationally expensive and requires significant resources, especially when dealing with multiple sources and nodes, as existing methods often scale rapidly with more complicated graphs.
Innovation Solution
A path-centric approach using an edge table and path table to iteratively build and update paths, flagging active and inactive paths, and selectively adding new paths while discarding non-shortest paths, allowing for efficient identification of shortest paths without node state storage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional shortest path algorithms are used to solve shortest path problems in complex graphs, then the shortest paths can be identified, but the computational resources required scale rapidly and become prohibitively expensive
Solution Approach 1:
The patent segments the graph problem into multiple independent shortest path problems by fixing one node as the source and finding shortest paths to all other nodes. This segmentation allows the use of efficient single-source shortest path algorithms rather than exhaustively solving the general shortest path problem between all node pairs, significantly reducing computational resource consumption while maintaining accuracy.
Solution Approach 2:
The patent performs preliminary actions by pre-calculating and storing shortest path information in a distance matrix during an initialization phase. This preliminary computation allows subsequent queries to be answered efficiently without re-computing entire shortest paths, reducing the computational resources needed for repeated shortest path identification tasks.
2Reliability
If more computing resources are allocated to solve shortest path problems in complicated graphs, then more accurate results can be obtained, but the resource requirements scale rapidly with graph complexity
Solution Approach 1:
The patent changes the parameter representation from storing complete path sequences to storing only distance values in a matrix format. This parameter transformation reduces the complexity of data structures needed while maintaining the reliability of shortest path information, as distances can be used to reconstruct paths when needed without storing all possible path combinations.
3Measurement precision
If all possible paths are evaluated to ensure the shortest path is found, then the most accurate shortest path is identified, but the computational time and resources increase significantly
Solution Approach 1:
The patent extracts only the essential information needed for shortest path identification by storing distance values in a matrix rather than evaluating and storing all possible paths. This extraction of critical data (distances between nodes) eliminates the need to process redundant path information, significantly reducing computational time while maintaining measurement accuracy through the use of proven shortest path algorithms.
Data Source
AI summary
Examples relate to identifying shortest paths. In one example, a computing device may: access an edge table that specifies, for each edge of a graph, an edge source, an edge destination, and an edge distance value; access a current path table that specifies paths between nodes of the graph and, for each path, a source node, a destination node, a distance, and a node path; identify each path included in the current path table as a shortest known path; and for each path having a destination node that matches an edge source node, add a new path to the current path table, the new path specifying: the source node as a new source; the edge destination as a new destination; a sum of the edge value and the path distance as a new distance; and the edge destination appended to the node path as a new node path.