Continuous Map Matching to Paths under Travel Time Constraints

2025-06-23

AI Summary

This paper addresses the continuous map matching problem under travel-time constraints: given a spatiotemporal measurement sequence and a road network graph with travel-time-weighted edges, the goal is to match each measurement to a continuous location on the graph such that consecutive matched points are reachable along graph edges within their temporal separation. To overcome the limited expressiveness of conventional discrete-candidate approaches, we propose the first exact algorithm supporting infinitely many continuous candidate positions, guaranteed to find a feasible, temporally consistent matching path whenever one exists. Our method integrates continuous geometric modeling of the road network with time-feasibility analysis via a novel segment–circle intersection data structure. Theoretically, it achieves time complexity of $O(k^2 n log nk)$ or $O(k n^lambda + n log^3 n)$, improving upon the baseline $O(k n^2)$. Extensive experiments on synthetic and real-world GTFS transit data demonstrate its efficiency and robustness.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

In this paper, we study the problem of map matching with travel time constraints. Given a sequence of $k$ spatio-temporal measurements and an embedded path graph with travel time costs, the goal is to snap each measurement to a close-by location in the graph, such that consecutive locations can be reached from one another along the path within the timestamp difference of the respective measurements. This problem arises in public transit data processing as well as in map matching of movement trajectories to general graphs. We show that the classical approach for this problem, which relies on selecting a finite set of candidate locations in the graph for each measurement, cannot guarantee to find a consistent solution. We propose a new algorithm that can deal with an infinite set of candidate locations per measurement. We prove that our algorithm always detects a consistent map matching path (if one exists). Despite the enlarged candidate set, we also demonstrate that our algorithm has superior running time in theory and practice. For a path graph with $n$ nodes, we show that our algorithm runs in $mathcal{O}(k^2 n log {nk})$ and under mild assumptions in $mathcal{O}(k n ^λ+ n log^3 n)$ for $λapprox 0.695$. This is a significant improvement over the baseline, which runs in $mathcal{O}(k n^2)$ and which might not even identify a correct solution. The performance of our algorithm hinges on an efficient segment-circle intersection data structure. We describe how to design and implement such a data structure for our application. In the experimental evaluation, we demonstrate the usefulness of our novel algorithm on a diverse set of generated measurements as well as GTFS data.

Problem

• Map matching with infinite candidate locations per measurement
• Ensuring consistent paths under travel time constraints
• Improving algorithm efficiency for large path graphs

Innovation

• Handles infinite candidate locations per measurement
• Ensures consistent map matching path detection
• Improves running time with efficient data structure