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We consider several variants of the map-matching problem, which seeks to find a path Q in graph G that has the smallest distance to a given trajectory P (which is likely not to be exactly on the graph). In a typical application setting, P models a noisy GPS trajectory from a person traveling on a road network, and the desired path Q should ideally correspond to the actual path in G that the person has traveled. Existing map-matching algorithms in the literature consider all possible paths in G as potential candidates for Q. We find solutions to the map-matching problem under different settings. In particular, we restrict the set of paths to shortest paths, or concatenations of shortest paths, in G. As a distance measure, we use the Fréchet distance, which is a suitable distance measure for curves since it takes the continuity of the curves into account.
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Finding Your Way: Shortest Paths on Networks
Traveling to different destinations is a major part of our lives. We visit a variety of locations both during our daily lives and when we are on vacation. How can we find the best way to navigate from one place to another? Perhaps we can test all of the different ways of traveling between two places, but another method is to use mathematics and computation to find a shortest path between them. In this article, we discuss how to construct shortest paths and introduce Dijkstra’s algorithm to minimize the total cost of a path, where the cost may be the travel distance, the travel time, or some other quantity. We also discuss how to use shortest paths in the real world to save time and increase traveling efficiency.
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- Award ID(s):
- 1922952
- PAR ID:
- 10335398
- Date Published:
- Journal Name:
- Frontiers for Young Minds
- Volume:
- 9
- ISSN:
- 2296-6846
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3389/frym.2021.631045
