# Minimizing Walking Length in Map Matching

Abstract : In this paper, we propose a geometric algorithm for a map matching problem. More specifically, we are given a planar graph, H, with a straight-line embedding in a plane, a directed polygonal curve, T, and a distance value $\varepsilon >0$. The task is to find a path, P, in H, and a parameterization of T, that minimize the sum of the length of walks on T and P whereby the distance between the entities moving along P and T is at most $\varepsilon$ε, at any time during the walks. It is allowed to walk forwards and backwards on T and edges of H. We propose an algorithm with $\mathcal {O}\left( mn \left( m+n\right) \log (mn)\right)$ time complexity and $\mathcal {O}\left( mn \left( m+n\right) \right)$ space complexity, where m (n, respectively) is the number of edges of H (of T, respectively). As we show, the algorithm can be generalized to work also for weighted non-planar graphs within the same time and space complexities.
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Conference papers
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Cited literature [15 references]

https://hal.inria.fr/hal-01446266
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Amin Gheibi, Anil Maheshwari, Jörg-Rüdiger Sack. Minimizing Walking Length in Map Matching. 1st International Conference on Theoretical Computer Science (TTCS), Aug 2015, Tehran, Iran. pp.105-120, ⟨10.1007/978-3-319-28678-5_8⟩. ⟨hal-01446266⟩

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