Honors College Theses

Date

2021

Major

Mathematics (B.S.)

Document Type and Release Option

Thesis (open access)

Faculty Mentor

Hua Wang

Abstract

Sensor placement has many applications and uses that can be seen everywhere you go.These include, but not limited to, monitoring the structural health of buildings and bridgesand navigating Unmanned Aerial Vehicles(UAV).We study ways that leads to efficient algorithms that will place as few as possible sen-sors to cover an entire area. We will tackle the problem from both 2-dimensional and3-dimensional points of view. Two famous related problems are discussed: the art galleryproblem and the terrain guarding problem. From the top view an area presents a 2-D im-age which will enable us to partition polygonal shapes and use graph theoretical results incoloring. We explore this approach in details and discuss potential generalizations. Wewill also look at the area from a side view and use methods from the terrain guarding prob-lem to determine where any more sensors should be placed. We provide a simple greedyalgorithm for this.Lastly, we briefly discuss the combination of the above techniques and potential furthergeneralizations to suit specific problems where the limitation of sensors (such as range andangle) are taken into consideration.

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