Shortest path algorithms have played a key role in the past century, paving the way for modern day GPS systems to find optimal routes along static systems in fractions of a second. One application of these algorithms includes optimizing the total distance of power lines (specifically in star topological configurations). Due to the relevancy of discovering well-connected electrical systems in certain areas, finding a minimum path that is able to account for geological features would have far-reaching consequences in lowering the cost of electric power transmission. We initialize our research by proving the convex hull as an effective bounding mechanism for star topological minimum path algorithms. Building off this bounding, we propose novel algorithms to manage certain cases that lack existing methods (weighted regions and obstacles) by discretizing Euclidean space into squares and combining pre-existing algorithms that calculate local minimums that we believe have a possibility of being the absolute minimum. We further designate ways to evaluate iterations necessary to reach some level of accuracy. Both of these novel algorithms fulfill certain niches that past literature does not cover.

中文翻译：

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加权区域和障碍物的最小路径星形拓扑算法

最短路径算法在上个世纪发挥了关键作用，为现代 GPS 系统在几分之一秒内沿着静态系统找到最佳路线铺平了道路。这些算法的一种应用包括优化电力线的总距离（特别是在星形拓扑配置中）。由于在某些地区发现连接良好的电力系统的相关性，找到能够解释地质特征的最小路径将对降低电力传输成​​本产生深远的影响。我们通过证明凸包作为星形拓扑最小路径算法的有效边界机制来初始化我们的研究。建立在这个边界上，我们提出了新的算法来管理某些缺乏现有方法（加权区域和障碍物）的情况，方法是将欧几里得空间离散为正方形，并结合计算我们认为有可能成为绝对最小值的局部最小值的预先存在的算法。我们进一步指定了评估达到某种精度水平所需的迭代的方法。这两种新颖的算法都满足了过去文献没有涵盖的某些领域。