Matching Items (2)
Description
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.
ContributorsNayeri, Peyman (Author) / Colbourn, Charles (Thesis advisor) / Konjevod, Goran (Thesis advisor) / Sen, Arunabha (Committee member) / Stanzione Jr, Daniel (Committee member) / Arizona State University (Publisher)
Created2011
Description
Exhaustive testing is generally infeasible except in the smallest of systems. Research
has shown that testing the interactions among fewer (up to 6) components is generally
sufficient while retaining the capability to detect up to 99% of defects. This leads to a
substantial decrease in the number of tests. Covering arrays are combinatorial objects
that guarantee that every interaction is tested at least once.
In the absence of direct constructions, forming small covering arrays is generally
an expensive computational task. Algorithms to generate covering arrays have been
extensively studied yet no single algorithm provides the smallest solution. More
recently research has been directed towards a new technique called post-optimization.
These algorithms take an existing covering array and attempt to reduce its size.
This thesis presents a new idea for post-optimization by representing covering
arrays as graphs. Some properties of these graphs are established and the results are
contrasted with existing post-optimization algorithms. The idea is then generalized to
close variants of covering arrays with surprising results which in some cases reduce
the size by 30%. Applications of the method to generation and test prioritization are
studied and some interesting results are reported.
has shown that testing the interactions among fewer (up to 6) components is generally
sufficient while retaining the capability to detect up to 99% of defects. This leads to a
substantial decrease in the number of tests. Covering arrays are combinatorial objects
that guarantee that every interaction is tested at least once.
In the absence of direct constructions, forming small covering arrays is generally
an expensive computational task. Algorithms to generate covering arrays have been
extensively studied yet no single algorithm provides the smallest solution. More
recently research has been directed towards a new technique called post-optimization.
These algorithms take an existing covering array and attempt to reduce its size.
This thesis presents a new idea for post-optimization by representing covering
arrays as graphs. Some properties of these graphs are established and the results are
contrasted with existing post-optimization algorithms. The idea is then generalized to
close variants of covering arrays with surprising results which in some cases reduce
the size by 30%. Applications of the method to generation and test prioritization are
studied and some interesting results are reported.
ContributorsKaria, Rushang Vinod (Author) / Colbourn, Charles J (Thesis advisor) / Syrotiuk, Violet (Committee member) / Richa, Andréa W. (Committee member) / Arizona State University (Publisher)
Created2015