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Automated Code Engine For Tensor Hypercontraction: Derivation, Optimization And Implementation Of Rank-Reduced Coupled Cluster Theories, Yao Zhao

Dissertations, Theses, and Capstone Projects

The ultimate goal of electronic structure theory is solving the electronic Schr¨odinger Equation. However, even accurate approximations of solving Schr¨odinger Equation, such as high order coupled cluster theories, require computational efforts that are too demanding to be applied on large chemical systems. This thesis tackles the problem of curse of dimensionality: how to reduce the time complexity of high-accuracy coupled cluster methods in order to accelerate computations of molecular energy. On one hand, we believe that low-rank approximation (i.e. Tensor HyperContraction) of high-order tensors appearing in coupled cluster theory is a promising way to achieve rank-reduced coupled cluster theory. On …

The Computational Complexity Of Some Games And Puzzles With Theoretical Applications, Vasiliki Despoina Mitsou

Dissertations, Theses, and Capstone Projects

The subject of this thesis is the algorithmic properties of one- and two-player

games people enjoy playing, such as Sudoku or Chess. Questions asked about puzzles

and games in this context are of the following type: can we design efficient computer

programs that play optimally given any opponent (for a two-player game), or solve

any instance of the puzzle in question?

We examine four games and puzzles and show algorithmic as well as intractability

results. First, we study the wolf-goat-cabbage puzzle, where a man wants to transport

a wolf, a goat, and a cabbage across a river by using a …

Scheduling And Resource Allocation In Wireless Sensor Networks, Yosef Alayev

Dissertations, Theses, and Capstone Projects

In computer science and telecommunications, wireless sensor networks are an active research area. Each sensor in a wireless sensor network has some pre-defined or on demand tasks such as collecting or disseminating data. Network resources, such as broadcast channels, number of sensors, power, battery life, etc., are limited. Hence, a schedule is required to optimally allocate network resources so as to maximize some profit or minimize some cost. This thesis focuses on scheduling problems in the wireless sensor networks environment. In particular, we study three scheduling problems in the wireless sensor networks: broadcast scheduling, sensor scheduling for area monitoring, and …