Time-Dependent Fastest Path Computation in Spatial Networks
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Solution Overview
Problem
Existing path computation techniques in spatial networks assume constant travel-times, failing to account for time-dependent changes due to traffic congestion, which leads to suboptimal path recommendations that do not vary with departure-time.
Innovation Solution
The method involves partitioning a road network graph into subgraphs with time-dependent edge weights, using a bidirectional time-dependent fastest path algorithm and hierarchical path finding techniques to precompute lower and upper-bound graphs, enabling efficient computation of the fastest path considering varying travel-times.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If constant edge weight assumptions are used in path computation, then computation speed is improved, but path accuracy deteriorates because time-dependent traffic variations are not captured
Solution Approach 1:
The patent applies dynamics by transitioning from static constant edge weights to dynamic time-dependent edge weights that vary with departure time. The system computes different paths based on when the traversal starts, allowing the network model to adapt to temporal variations in traffic conditions. This is achieved through time-dependent shortest path algorithms that consider the start time of path traversal.
Solution Approach 2:
The patent uses preliminary action through precomputation of all-pairs shortest paths and construction of lower-bound graphs before actual path queries. By precomputing distance labels and hierarchical structures in advance, the system prepares data structures that enable fast online queries while accounting for time-dependent variations, thus improving both speed and accuracy.
2Measurement precision
If time-dependent edge weights are used to capture traffic variations, then path accuracy is improved, but computation complexity increases
Solution Approach 1:
The patent applies segmentation by dividing the road network into hierarchical levels and partitioning it into subgraphs. This hierarchical decomposition allows the complex time-dependent shortest path problem to be broken down into smaller, more manageable subproblems that can be solved efficiently at different levels of the hierarchy, reducing overall computational complexity.
Solution Approach 2:
The patent uses parameter changes by transforming the time-dependent shortest path problem into a series of static shortest path problems through parameter substitution. By using lower-bound graphs and distance labels as parameters, the system simplifies the complex time-dependent computations while maintaining accuracy, effectively changing the problem parameters to make computation more tractable.
3Reliability
If exact time-dependent shortest path algorithms are used, then path optimality is improved, but computation time increases
Solution Approach 1:
The patent applies preliminary action through extensive precomputation of all-pairs shortest paths, lower-bound graphs, and distance labels before online queries. By preparing these data structures in advance, the system ensures that exact time-dependent shortest paths can be found quickly during online operation, thus achieving both optimality and fast response times.
Solution Approach 2:
The patent uses dynamics by implementing algorithms that adapt to the specific query parameters (source, destination, departure time) while maintaining exactness. The time-dependent shortest path computation dynamically adjusts based on the departure time provided, ensuring optimal paths are found for each specific scenario without requiring exhaustive search.
Data Source
AI summary
With real-world spatial networks the edge travel-times are time-dependent, where the arrival-time to an edge determines the actual travel-time on the edge. To speed up the path computation, exact and approximate techniques for computation of the fastest path in time-dependent spatial networks are presented. An exact fastest path computation technique based on a time-dependent A* search can significantly improve the computation time and storage complexity of existing approaches. Moreover, for applications with which approximate fastest path is acceptable, the approximate fastest path computation technique can improve the computation time by an order of magnitude while maintaining high accuracy (e.g., with only 7% increase in travel-time of the computed path on average). With experiments using real data-sets (including a variety of large spatial networks with real traffic data) the efficacy of the disclosed techniques for online fastest path computation is demonstrated.