We present an efficient algorithm for solving an interval coverage problem. Given n intervals of the same length on a line L and a line segment B on L, we want to move the intervals along L such that every point of B is covered by at least one interval and the sum of the moving distances of all intervals is minimized. As a fundamental computational geometry problem, it has applications in mobile sensor barrier coverage in wireless sensor networks. The previous work gave an O(n2) time algorithm for it. In this thesis, by discovering many interesting observations and developing new algorithmic techniques, we present an O(nlogn) time algorithm for this problem. We also show that Ω(n log n) is the lower bound for the time complexity. Therefore, our algorithm is optimal. Further, our observations and algorithmic techniques may be useful for solving other related problems.

Ordinal coefficient alpha is a newly derived non-parametric reliability estimate. As with any point estimate, ordinal coefficient alpha is merely an estimate of a population parameter and tends to vary from sample to sample. Researchers report the confidence interval to provide readers with the amount of precision obtained. Several methods with differing computational approaches exist for confidence interval estimation for alpha, including the Fisher, Feldt, Bonner, and Hakstian and Whalen (HW) techniques. Overall, coverage rates for the various methods were unacceptably low with the Fisher method as the highest performer at 62%. Because of the poor performance across all four confidence interval methods, a need exists to develop a method which works well for ordinal coefficient alpha.