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arXiv · 2407.19304

Map-Matching Queries under Fréchet Distance on Low-Density Spanners

Kevin Buchin·Maike Buchin·Joachim Gudmundsson·Aleksandr Popov·Sampson Wong
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Abstract

Map matching is a common task when analysing GPS tracks, such as vehicle trajectories. The goal is to match a recorded noisy polygonal curve to a path on the map, usually represented as a geometric graph. The Fréchet distance is a commonly used metric for curves, making it a natural fit. The map-matching problem is well-studied, yet until recently no-one tackled the data structure question: preprocess a given graph so that one can query the minimum Fréchet distance between all graph paths and a polygonal curve. Recently, Gudmundsson, Seybold, and Wong [SODA 2023, arXiv:2211.02951] studied this problem for arbitrary query polygonal curves and $c$-packed graphs. In this paper, we instead require the graphs to be $λ$-low-density $t$-spanners, which is significantly more representative of real-world networks. We also show how to report a path that minimises the distance efficiently rather than only returning the minimal distance, which was stated as an open problem in their paper.

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Kevin Buchin, Maike Buchin, Joachim Gudmundsson, Aleksandr Popov, Sampson Wong. 2024-07-27. Map-Matching Queries under Fréchet Distance on Low-Density Spanners. https://arxiv.org/abs/2407.19304

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