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Creators/Authors contains: "Holmgren, Benjamin"

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  1. ; ; ; ; (, 35th Canadian Conference on Computational Geometry)
    Accepted Manuscript Full Text Available
  2. ; ; ; ; (, CCCG)
    The Fréchet distance is often used to measure distances between paths, with applications in areas ranging from map matching to GPS trajectory analysis to hand- writing recognition. More recently, the Fréchet distance has been generalized to a distance between two copies of the same graph embedded or immersed in a metric space; this more general setting opens up a wide range of more complex applications in graph analysis. In this paper, we initiate a study of some of the fundamental topological properties of spaces of paths and of graphs mapped to R^n under the Fréchet distance, in an eort to lay the theoretical groundwork for understanding how these distances can be used in practice. In particular, we prove whether or not these spaces, and the metric balls therein, are path-connected. 
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    Accepted Manuscript Full Text Available
  3. ; ; ; ; (, Young Researcher's Forum (CG Week))
    We examine topological properties of spaces of paths and graphs mapped to $$\R^d$$ under the Fr\'echet distance. We show that these spaces are path-connected if the map is either continuous or an immersion. If the map is an embedding, we show that the space of paths is path-connected, while the space of graphs only maintains this property in dimensions four or higher. 
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    Accepted Manuscript Full Text Available