Fastest Route Computation Using Graph Separators and Heuristics
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Solution Overview
Problem
Current navigation systems face challenges in efficiently computing the fastest travel routes in large road networks under dynamic traffic conditions, requiring significant data storage and processing time.
Innovation Solution
The method utilizes graph separators in a preprocessing stage to determine an effective heuristic function for the A* algorithm, reducing the number of graph vertices traversed and enabling quicker computation of fastest paths.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If current state-of-the-art methods (Contraction Hierarchy) are used for fastest route computation, then routing accuracy is improved, but data storage requirements and processing complexity increase significantly
Solution Approach 1:
The patent extracts only the essential components needed for route computation by utilizing pre-computed all-pairs shortest paths on a contracted graph. Instead of storing complete detailed road network data, the system extracts and stores only the distance matrix and route information necessary for answering queries, significantly reducing storage requirements while maintaining routing accuracy.
Solution Approach 2:
The patent applies preliminary action by pre-computing all-pairs shortest paths and storing them in a distance matrix before actual routing queries are executed. This preprocessing step enables the system to answer routing queries efficiently without performing complex real-time computations, trading off initial processing time for faster query response and reduced storage needs.
2Measurement precision
If exhaustive search of all possible routes is performed, then routing accuracy is improved, but computation time increases significantly
Solution Approach 1:
The patent performs preliminary computation of all-pairs shortest paths using algorithms like Floyd-Warshall or Johnson's algorithm before routing queries are submitted. This pre-computation stores the optimal path information in a distance matrix, enabling O(1) lookup for routing queries and eliminating the need for exhaustive search during actual operations.
Solution Approach 2:
The patent segments the routing problem into two distinct phases: an offline preprocessing phase where all-pairs shortest paths are computed and stored, and an online query phase where routing is determined by simple matrix lookup. This segmentation allows complex computations to be performed once beforehand, transforming the online problem into a simple retrieval operation.
Data Source
AI summary
A method and system that utilizes an admissible heuristic to determine the fastest-path between two points on a road map is disclosed. The method and system are based in part on a set of separators disposed on the map and represented by line segments, either independent or organized into hierarchical tree structures and based on recursive spatial subdivision. A preprocessing step computes a vector of values per road junction based on the separators that is then stored with the map and used to efficiently compute a high-quality heuristic to be used at a query stage. The heuristic scales well to any map size, resulting in a very efficient determination of fastest-path queries between points at all distances. The implementation is economically feasible and the resulting query speeds are significantly faster than other known heuristics and other state-of-the-art systems used for computing fastest-paths on maps.