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Full-Text Articles in Discrete Mathematics and Combinatorics
Recent Advances In Compressed Sensing: Discrete Uncertainty Principles And Fast Hyperspectral Imaging, Megan E. Lewis
Recent Advances In Compressed Sensing: Discrete Uncertainty Principles And Fast Hyperspectral Imaging, Megan E. Lewis
Theses and Dissertations
Compressed sensing is an important field with continuing advances in theory and applications. This thesis provides contributions to both theory and application. Much of the theory behind compressed sensing is based on uncertainty principles, which state that a signal cannot be concentrated in both time and frequency. We develop a new discrete uncertainty principle and use it to demonstrate a fundamental limitation of the demixing problem, and to provide a fast method of detecting sparse signals. The second half of this thesis focuses on a specific application of compressed sensing: hyperspectral imaging. Conventional hyperspectral platforms require long exposure times, which …
A Group Theoretic Tabu Search Approach To The Traveling Salesman Problem, Shane N. Hall
A Group Theoretic Tabu Search Approach To The Traveling Salesman Problem, Shane N. Hall
Theses and Dissertations
The traveling salesman problem (TSP) is a combinatorial optimization problem that is mathematically modeled as a binary integer program. The TSP is a very important problem for the operations research academician and practitioner. This research demonstrates a Group Theoretic Tabu Search (GTTS) Java algorithm for the TSP. The tabu search metaheuristic continuously finds near-optimal solutions to the TSP under various different implementations. Algebraic group theory offers a more formal mathematical setting to study the TSP providing a theoretical foundation for describing tabu search. Specifically, this thesis uses the Symmetric Group on n letters, S(n), which is the set of all …