This paper presents the results of using sequential analysis to find increment sequences that minimize the average running time of Shellsort, for array sizes up to several thousand elements. The obtained sequences outperform by about 3% the best ones known so far, and there is a plausible evidence that they are the optimal ones.

We study sorting algorithms based on randomized roundrobin comparisons. Specifically, we study Spin-the-bottle sort, where comparisons are unrestricted, and Annealing sort, where comparisons are restricted to a distance bounded by a temperature parameter. Both algorithms are simple, randomized, data-oblivious sorting algorithms, which are useful in privacy-preserving computations, but, as we show, Annealing sort is much more efficient. We show that there is an input permutation that causes Spin-the-bottle sort to require Ω(n 2 log n) expected time in order to succeed, and that in O(n 2 log n) time this algorithm succeeds with high probability for any input. We also show there is an specification of Annealing sort that runs in O(n log n) time and succeeds with very high probability. 1

This work addresses computational problems related to the implementation of Victor and Purpura’s spike- time distance metric for temporal point process data. Three computational algorithms are presented that facilitate the calculation of spike-time distance. In addition, recommendations for penalty parameters are provided, and several properties and extensions of the spike-time metric, and of point pattern distance metrics more generally, are discussed. Applications include the formation of prototype point patterns that can be used for describing a typical point pattern in a collection of point patterns, and various clustering algorithms that can be modified for application to point process data through the use of spiketime distance and prototype patterns. Extensions of these techniques to m u ltidimensional p o int p atterns are also addressed.