In the age of growing technology, Computer Science (CS) professionals have come into high demand. However, despite popular demand there are not enough computer scientists to fill these roles. The current demographic of computer scientists consists mainly of white men. This apparent gender gap must be addressed to promote diversity and inclusivity in a career that requires high creativity and innovation. To understand what enforces gender stereotypes and the gender gap within CS, survey and interview data were collected from both male and female senior students studying CS and those who have left the CS program at Arizona State University. Students were asked what experiences either diminished or reinforced their sense of belonging in this field as well as other questions related to their involvement in CS. Interview and survey data reveal a lack of representation within courses as well as lack of peer support are key factors that influence the involvement and retention of students in CS, especially women. This data was used to identify key factors that influence retention and what can be done to remedy the growing deficit of professionals in this field.
Firstly, hash families in which the associated property is satisfied at least some number lambda times are considered, called higher-index, which guarantees redundancy when constructing t-restrictions. Some direct and optimal constructions of hash families of higher index are given. A new recursive construction is established that generalizes previous results and generates higher-index PHFs with more columns. Probabilistic methods are employed to obtain an upper bound on the optimal size of higher-index PHFs when the number of columns is large. A new deterministic algorithm is developed that generates such PHFs meeting this bound, and computational results are reported.
Secondly, a restriction on the structure of PHFs is introduced, called fractal, a method from Blackburn. His method is extended in several ways; from homogeneous hash families (every row has the same number of symbols) to heterogeneous ones; and to distributing hash families, a relaxation of the predicate for PHFs. Recursive constructions with fractal hash families as ingredients are given, and improve upon on the best-known sizes of many PHFs.
Thirdly, a method of Colbourn and Lanus is extended in which they horizontally copied a given hash family and greedily applied transformations to each copy. Transformations of existential t-restrictions are introduced, which allow for the method to be applicable to any t-restriction having structure like those of hash families. A genetic algorithm is employed for finding the "best" such transformations. Computational results of the GA are reported using PHFs, as the number of transformations permitted is large compared to the number of symbols. Finally, an analysis is given of what trade-offs exist between computation time and the number of t-sets left not satisfying the predicate.