Queue-mergesort is recently introduced by Golin and Sedgewick as an optimal variant of mergesorts in the worst case. In this paper, we present a complete analysis of the cost distribution of queue-mergesort, including the best, average and variance cases. The asymptotic normality of its cost is also established under the uniform permutation model. We address the corresponding optimality problems and show that if we fix the merging scheme then the optimal mergesort as far as the average number of comparisons is concerned is to divide as evenly as possible at each recursive stage (top-down mergesort). On the other hand, the variance of queue-mergesort reaches asymptotically the minimum value. We also characterize a class of mergesorts with the latter property. A comparative discussion is given on the probabilistic behaviors of top-down mergesort, bottom-up mergesort and queue-mergesort. We derive an "invariance principle" for asymptotic linearity of divide-and-conquer recurrences based on general "power-of-two" rules of which the underlying dividing rule of queue-mergesort is a special case. These analyses reveal an interesting algorithmic feature for general "power-of-two" rules.

I declare that this thesis is my own account of my research and contains as its main content work which has not previously been submitted for a degree at any tertiary education institution. Joel Kelso ii The purported advantages of Visual Programming, as applied to general purpose programming languages, have remained largely unfulfilled. The essence of this thesis is that functional programming languages have at least one natural visual representation, and that a useful programming environment can be based upon this representation. This thesis describes the implementation of a Visual Functional Programming Environment (VFPE). The programming environment has several significant features. • The environment includes a program editor that is inherently

Sorting is a fundamental algorithmic task. Many general-purpose sorting algorithms have been developed, but efficiency gains can be achieved by designing algorithms for specific kinds of data, such as strings. In previous work we have shown that our burstsort, a trie-based algorithm for sorting strings, is for large data sets more efficient than all previous algorithms for this task. In this paper we re-evaluate some of the implementation details of burstsort, in particular the method for managing buckets held at leaves. We show that better choice of data structures further improves the efficiency, at a small additional cost in memory. For sets of around 30,000,000 strings, our improved burstsort is nearly twice as fast as the previous best sorting algorithm.