Bidirectional Search for Shortest Path in Dense Graphs
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Solution Overview
Problem
The Floyd algorithm used for determining shortest paths in dense graphs has high spatiotemporal complexity, resulting in low search efficiency.
Innovation Solution
A method involving a forward search and a reverse search in a target undirected weighted graph to determine an initial encounter node, which allows for the identification of the shortest path from a start point to a target point without exponential growth of expansion nodes, thereby reducing complexity and improving efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the Floyd algorithm is used to determine the shortest path in a dense graph, then the shortest path can be found, but the spatiotemporal complexity is high and search efficiency is low
Solution Approach 1:
The patent divides the single-direction search process into two separate searches: a forward search from the start node and a reverse search from the target node. This segmentation allows each search to explore only half the graph space needed for a complete single-direction search, reducing the number of nodes that need to be expanded and improving search efficiency while maintaining shortest path accuracy.
Solution Approach 2:
The patent applies reverse search by performing a search from the target node back to the start node, which is the opposite direction of the conventional forward search. This inversion allows the algorithm to meet in the middle, reducing the search space and computational complexity while still finding the optimal shortest path.
2Productivity
If forward search and reverse search are performed to determine the initial encounter node, then the spatiotemporal complexity is reduced, but the algorithm complexity increases
Solution Approach 1:
The patent merges the forward search results and reverse search results at the initial encounter node to construct the complete shortest path. By combining the path from start to encounter node with the path from encounter node to target, the algorithm achieves efficient search while maintaining manageable complexity through systematic integration of the two search directions.
Solution Approach 2:
The patent performs preliminary actions by conducting forward and reverse searches simultaneously from opposite directions, establishing meeting points before the full path is constructed. This preliminary exploration from both directions allows the algorithm to identify the initial encounter node early, reducing the overall search space and computational requirements.
Data Source
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AI summary
Disclosed are a method, apparatus, electronic device, and storage medium. The method includes: determining a target undirected weighted graph corresponding to a target area from a start point to a target point, which includes a plurality of nodes, edges connected between the nodes, and cost weights respectively corresponding to the edges; performing a forward search from a start node corresponding to the start point and a reverse search from a target node corresponding to the target point based on the cost weights respectively corresponding to the edges of each node, to determine an initial encounter node for the forward and reverse searches; and determining a target shortest path from the start point to the target point based on the initial encounter node. Thus, exponential growth of expansion nodes in a middle part can be avoided, reducing spatiotemporal complexity of the search and improving efficiency of determining a shortest path.