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Award ID contains: 1661530

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  1. ; ; (, 21st International Workshop on Algorithms in Bioinformatics (WABI 2021))
    null (Ed.)
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  2. ; ; ; ; ; ; ; ; (, Computational Geometry)
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  3. (, CCCG '18: Thirtieth Canadian Conference on Computational Geometry)
    Topological Data Analysis (TDA) studies the shape of data. A common topological descriptor is the persistence diagram, which encodes topological features in a topological space at different scales. Turner, Mukeherjee, and Boyer showed that one can reconstruct a simplicial complex embedded in R^3 using persistence diagrams generated from all possible height filtrations (an uncountably infinite number of directions). In this paper, we present an algorithm for reconstructing plane graphs K=(V,E) in R^2 , i.e., a planar graph with vertices in general position and a straight-line embedding, from a quadratic number height filtrations and their respective persistence diagrams. 
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