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Full-Text Articles in Physical Sciences and Mathematics
Algorithm For Generating Derivative Structures, Gus L. W. Hart, Rodney W. Forcade
Algorithm For Generating Derivative Structures, Gus L. W. Hart, Rodney W. Forcade
Faculty Publications
We present an algorithm for generating all derivative superstructures--for arbitrary parent structures and for any number of atom types. This algorithm enumerates superlattices and atomic configurations in a geometry-independent way. The key concept is to use the quotient group associated with each superlattice to determine all unique atomic configurations. The run time of the algorithm scales linearly with the number of unique structures found.
A Hike Through The Forest: The Knapsack Problem In Graph Theory, Bridget K. Druken
A Hike Through The Forest: The Knapsack Problem In Graph Theory, Bridget K. Druken
Senior Honors Projects
Graph theory is a branch of mathematics which studies graphs a collection of a set of edges and vertices used to sometimes model structures. My interest in graph theory began last semester in a math/computer science course entitled “Discrete Structures." One aspect which makes graph theory an appealing area to research is the amount of understanding that comes from a relatively short amount of time spent learning the subject material. The visual appeal of being able to draw a graph along practical applications that surface daily make graph theory a prime candidate for further research. Through research of the history …
Topological And Categorical Properties Of Binary Trees, Homeira Pajoohesh
Topological And Categorical Properties Of Binary Trees, Homeira Pajoohesh
Publications and Research
Binary trees are very useful tools in computer science for estimating the running time of so-called comparison based algorithms, algorithms in which every action is ultimately based on a prior comparison between two elements. For two given algorithms A and B where the decision tree of A is more balanced than that of B, it is known that the average and worst case times of A will be better than those of B, i.e., ₸A(n) ≤₸B(n) and TWA (n)≤TWB (n). Thus the most balanced and the most imbalanced binary trees play a main role. Here we consider them as semilattices …
An Energy-Aware Multilevel Clustering Algorithm For Wireless Sensor Networks, Xinfang Yan, Jiangtao Xi, Joe F. Chicharo, Yanguang Yu
An Energy-Aware Multilevel Clustering Algorithm For Wireless Sensor Networks, Xinfang Yan, Jiangtao Xi, Joe F. Chicharo, Yanguang Yu
Faculty of Informatics - Papers (Archive)
Clustering sensors nodes as the basic of routing is an efficient mechanism for prolonging the lifetime of wireless sensor networks. In this paper, the high-efficient multilevel clustering is abstracted as a root tree which has the performances of the minimal relay set and the maximal weight according to graph theory. A mathematical model for the clustering virtual backbone is built. Based on the model, an algorithm called energy-aware multilevel clustering (EAMC) is proposed. The EAMC can reduce the number of relays used for data transmission by minimizing the amount of the nodes in the root tree (that is cluster-head). Furthermore, …