Finding the optimal solution to a problem with an enormous search space can be challenging. Unless a combinatorial construction technique is found that also guarantees the optimality of the resulting solution, this could be an infeasible task. If such a technique is unavailable, different heuristic methods are generally used to…
Finding the optimal solution to a problem with an enormous search space can be challenging. Unless a combinatorial construction technique is found that also guarantees the optimality of the resulting solution, this could be an infeasible task. If such a technique is unavailable, different heuristic methods are generally used to improve the upper bound on the size of the optimal solution. This dissertation presents an alternative method which can be used to improve a solution to a problem rather than construct a solution from scratch. Necessity analysis, which is the key to this approach, is the process of analyzing the necessity of each element in a solution. The post-optimization algorithm presented here utilizes the result of the necessity analysis to improve the quality of the solution by eliminating unnecessary objects from the solution. While this technique could potentially be applied to different domains, this dissertation focuses on k-restriction problems, where a solution to the problem can be presented as an array. A scalable post-optimization algorithm for covering arrays is described, which starts from a valid solution and performs necessity analysis to iteratively improve the quality of the solution. It is shown that not only can this technique improve upon the previously best known results, it can also be added as a refinement step to any construction technique and in most cases further improvements are expected. The post-optimization algorithm is then modified to accommodate every k-restriction problem; and this generic algorithm can be used as a starting point to create a reasonable sized solution for any such problem. This generic algorithm is then further refined for hash family problems, by adding a conflict graph analysis to the necessity analysis phase. By recoloring the conflict graphs a new degree of flexibility is explored, which can further improve the quality of the solution.
Leonard Hayflick studied the processes by which cells age during the twentieth and twenty-first centuries in the United States. In 1961 at the Wistar Institute in the US, Hayflick researched a phenomenon later called the Hayflick Limit, or the claim that normal human cells can only divide forty to sixty…
Leonard Hayflick studied the processes by which cells age during the twentieth and twenty-first centuries in the United States. In 1961 at the Wistar Institute in the US, Hayflick researched a phenomenon later called the Hayflick Limit, or the claim that normal human cells can only divide forty to sixty times before they cannot divide any further. Researchers later found that the cause of the Hayflick Limit is the shortening of telomeres, or portions of DNA at the ends of chromosomes that slowly degrade as cells replicate. Hayflick used his research on normal embryonic cells to develop a vaccine for polio, and from HayflickÕs published directions, scientists developed vaccines for rubella, rabies, adenovirus, measles, chickenpox and shingles.
Although best known for his work with the fruit fly, for which he earned a Nobel Prize and the title "The Father of Genetics," Thomas Hunt Morgan's contributions to biology reach far beyond genetics. His research explored questions in embryology, regeneration, evolution, and heredity, using a variety of approaches.
