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   Cecire, Kenneth; Bilow, Uta (June 2020, EPS-HEP2019)

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2. The 1st International Workshop on Machine Reasoning: International Machine Reasoning Conference (MRC 2021)

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   Zhang, Yongfeng; Zhang, Min; Chen, Hanxiong; Chen, Xu; Chen, Xianjie; Gan, Chuang; Sun, Tong; Dong, Xin Luna (March 2021, WSDM '21: Proceedings of the 14th ACM International Conference on Web Search and Data Mining)

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3. Leibniz International Proceedings in Informatics (LIPIcs):39th International Symposium on Computational Geometry (SoCG 2023)

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   Agarwal, Pankaj K; Ezra, Esther (January 2023, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Chambers, Erin W; Gudmundsson, Joachim (Ed.)

   Let ℬ be a set of n unit balls in ℝ³. We present a linear-size data structure for storing ℬ that can determine in O^*(n^{1/2}) time whether a query line intersects any ball of ℬ and report all k such balls in additional O(k) time. The data structure can be constructed in O(n log n) time. (The O^*(⋅) notation hides subpolynomial factors, e.g., of the form O(n^ε), for arbitrarily small ε > 0, and their coefficients which depend on ε.) We also consider the dual problem: Let ℒ be a set of n lines in ℝ³. We preprocess ℒ, in O^*(n²) time, into a data structure of size O^*(n²) that can determine in O^*(1) time whether a query unit ball intersects any line of ℒ, or report all k such lines in additional O(k) time. 

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4. Leibniz International Proceedings in Informatics (LIPIcs):36th International Symposium on Computational Geometry (SoCG 2020)

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   Ameer, Safwa; Gibson-Lopez, Matt; Krohn, Erik; Soderman, Sean; Wang, Qing (June 2020, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Cabello, Sergio; Chen, Danny Z. (Ed.)

   In this paper, we consider the Visibility Graph Recognition and Reconstruction problems in the context of terrains. Here, we are given a graph G with labeled vertices v₀, v₁, …, v_{n-1} such that the labeling corresponds with a Hamiltonian path H. G also may contain other edges. We are interested in determining if there is a terrain T with vertices p₀, p₁, …, p_{n-1} such that G is the visibility graph of T and the boundary of T corresponds with H. G is said to be persistent if and only if it satisfies the so-called X-property and Bar-property. It is known that every "pseudo-terrain" has a persistent visibility graph and that every persistent graph is the visibility graph for some pseudo-terrain. The connection is not as clear for (geometric) terrains. It is known that the visibility graph of any terrain T is persistent, but it has been unclear whether every persistent graph G has a terrain T such that G is the visibility graph of T. There actually have been several papers that claim this to be the case (although no formal proof has ever been published), and recent works made steps towards building a terrain reconstruction algorithm for any persistent graph. In this paper, we show that there exists a persistent graph G that is not the visibility graph for any terrain T. This means persistence is not enough by itself to characterize the visibility graphs of terrains, and implies that pseudo-terrains are not stretchable. 

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5. International Masterclasses: Forward from Pandemic

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   Bilow, Uta; Cecire, Kenneth (November 2022, ICHEP 2022)