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We present methods for simplifying the geometry of polygonal obstacles as a preprocessing step to solving obstacle‐avoiding Steiner network problems in the plane. The methods reduce the total number of vertices and edges that need to be considered for the given obstacles, and their use is expected to significantly improve the efficiency of exact algorithms for solving a range of practical Steiner network problems in obstacle environments. Included are methods for extending obstacles (via a new padding method and a backfilling procedure from the literature), and various methods for simplifying obstacles, including new methods called bounding and eliminating. We show that these methods reduce the total number of obstacle vertices and edges by performing experiments on obstacles with up to 100 vertices in the presence of up to 100 terminals. The experiments utilize a modified version of a known algorithm for quickly generating large numbers of "random" polygons with hundreds of vertices. Corresponding datasets and implementations have been made available on GitHub. [ABSTRACT FROM AUTHOR]

As surges in the COVID‐19 pandemic have continued worldwide, severe acute respiratory syndrome coronavirus 2 (SARS‐CoV‐2) has mutated, spawning several new variants, and impacting, to various degrees, transmission, disease severity, diagnostics, therapeutics, and natural and vaccine‐induced immunity. Baylor Scott & White Health has implemented, along with laboratory diagnosis, SARS‐CoV‐2 sequencing to identify variants in its geographical service area. We analyzed virus sequencing results of specimens collected across Central Texas and found dramatic changes in variant distribution in the first half of 2021. The alpha variant (B 1.1.7) became predominant at week 13 and continued dominance until week 25. A growth rate of 1.20 (R2 = 0.92) for the first 15 weeks was noted and this growth gradually declined to −0.55 (R2 = 0.99) for the final 13 weeks. Currently, B.1.1.7 is being displaced with B.1.617.2 at a 0.58 growth rate (R2 = 0.97). We also investigated vaccine breakthrough cases (VBCs) within our healthcare system and present clinical data on 28 symptomatic patients. [ABSTRACT FROM AUTHOR]

We present a new exact algorithm for computing minimum 2‐edge‐connected Steiner networks in the Euclidean plane. The algorithm is based on the GeoSteiner framework for computing minimum Steiner trees in the plane. Several new geometric and topological properties of minimum 2‐edge‐connected Steiner networks are developed and incorporated into the new algorithm. Comprehensive experimental results are presented to document the performance of the algorithm which can reliably compute exact solutions to randomly generated instances with up to 50 terminals—doubling the range of existing exact algorithms. Finally, we discuss the appearance of Hamiltonian cycles as solutions to the minimum 2‐edge‐connected Steiner network problem. [ABSTRACT FROM AUTHOR]