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Shortest path algorithms have played a key role in the past century, pavingthe way for modern day GPS systems to find optimal routes along static systemsin fractions of a second. One application of these algorithms includesoptimizing the total distance of power lines (specifically in star topologicalconfigurations). Due to the relevancy of discovering well-connected electricalsystems in certain areas, finding a minimum path that is able to account forgeological features would have far-reaching consequences in lowering the costof electric power transmission. We initialize our research by proving theconvex hull as an effective bounding mechanism for star topological minimumpath algorithms. Building off this bounding, we propose novel algorithms tomanage certain cases that lack existing methods (weighted regions andobstacles) by discretizing Euclidean space into squares and combiningpre-existing algorithms that calculate local minimums that we believe have apossibility of being the absolute minimum. We further designate ways toevaluate iterations necessary to reach some level of accuracy. Both of thesenovel algorithms fulfill certain niches that past literature does not cover.

Minimum Path Star Topology Algorithms for Weighted Regions and Obstacles