Analysis of Quickselect under Yaroslavskiy's Dual-Pivoting Algorithm

There is excitement within the algorithms community about a new partitioning method introduced by Yaroslavskiy. This algorithm renders Quicksort slightly faster than the case when it runs under classic partitioning methods. We show that this improved performance in Quicksort is not sustained in Quickselect; a variant of Quicksort for finding order statistics. We investigate the number of comparisons made by Quickselect to find a key with a randomly selected rank under Yaroslavskiy's algorithm. This grand averaging is a smoothing operator over all individual distributions for specific fixed order statistics. We give the exact grand average. The grand distribution of the number of comparison (when suitably scaled) is given as the fixed-point solution of a distributional equation of a contraction in the Zolotarev metric space. Our investigation shows that Quickselect under older partitioning methods slightly outperforms Quickselect under Yaroslavskiy's algorithm, for an order statistic of a random rank. Similar results are obtained for extremal order statistics, where again we find the exact average, and the distribution for the number of comparisons (when suitably scaled). Both limiting distributions are of perpetuities (a sum of products of independent mixed continuous random variables).Comment: full version with appendices; otherwise identical to Algorithmica versio

Analysis of pivot sampling in dual-pivot Quicksort: A holistic analysis of Yaroslavskiy's partitioning scheme

The final publication is available at Springer via http://dx.doi.org/10.1007/s00453-015-0041-7The new dual-pivot Quicksort by Vladimir Yaroslavskiy-used in Oracle's Java runtime library since version 7-features intriguing asymmetries. They make a basic variant of this algorithm use less comparisons than classic single-pivot Quicksort. In this paper, we extend the analysis to the case where the two pivots are chosen as fixed order statistics of a random sample. Surprisingly, dual-pivot Quicksort then needs more comparisons than a corresponding version of classic Quicksort, so it is clear that counting comparisons is not sufficient to explain the running time advantages observed for Yaroslavskiy's algorithm in practice. Consequently, we take a more holistic approach and give also the precise leading term of the average number of swaps, the number of executed Java Bytecode instructions and the number of scanned elements, a new simple cost measure that approximates I/O costs in the memory hierarchy. We determine optimal order statistics for each of the cost measures. It turns out that the asymmetries in Yaroslavskiy's algorithm render pivots with a systematic skew more efficient than the symmetric choice. Moreover, we finally have a convincing explanation for the success of Yaroslavskiy's algorithm in practice: compared with corresponding versions of classic single-pivot Quicksort, dual-pivot Quicksort needs significantly less I/Os, both with and without pivot sampling.Peer ReviewedPostprint (author's final draft

The Travels and Translations of Three African Anglican Missionaries, 1890-1930

Histories of the modern missionary movement frequently assert that converts were more successful missionaries than Europeans yet details of their work remain sparse. This article examines influential factors in the spread of Christianity in Sub-Saharan Africa in two ways. It explores the complex and variable processes through life sketches of the African missionaries, Bernard Mizeki, Leonard Kamungu and Apolo Kivebulaya, who worked with the Anglican mission agencies SPG, UMCA and CMS, respectively. It identifies common elements for further scrutiny including the role of travel, translation and communication, and the development of continental centres of Christianity and the trajectories between them and local hubs of mission activity. The transnational turn of contemporary history is employed and critiqued to scrutinise the relations between the local and global in order to comprehend the appeal of Christianity in the colonial era

Remote manipulator dynamic simulation

A simulator to generate the real time visual scenes required to perform man in the loop investigations of remote manipulator application and design concepts for the space shuttle is described. The simulated remote manipulator consists of a computed display system that uses a digital computer, the electronic scene generator, an operator's station, and associated interface hardware. A description of the capabilities of the implemented simulation is presented. The mathematical models and programs developed for the simulation are included

Probation Officer Role Orientation, Helping Alliance, and Probationer Readiness for Change:The Impact on Juvenile Offender Recidivism

The aim of the present study was to investigate the individual and collective influences of officer role orientation, the helping alliance, and probationer readiness for change on the reduction of recidivism rates among juvenile offenders. Archival data from a sample of 33 officers and 314 juvenile probationers were examined. Data included an officer demographic form, a probationer demographic and recidivism form, the Subjective Role Orientation and Strategy Scale, the Dual Role Inventory-Revised Probationer Version, and the University of Rhode Island Change Assessment. Results demonstrated that the sample of probation officers overwhelmingly adopted a balanced approach to supervision. This limited a further utilization of this variable for prediction purposes. Probationers who reported a more positive helping alliance with their officers evidenced lower recidivism rates of probation violations and new charges. Readiness for change scores were higher if violations had been handled by the probation department, if increasingly punitive sanctions were evident, and/or if the probationer evidenced a perceived problem or psychological diagnosis. The findings suggest probation departments could benefit from training officers to recognize and strengthen the helping alliance with their probationers, from utilizing sanctions issued by the probation officer to increase readiness for change, and from assisting probationers in identifying an internalized problem that results in interval motivation

Dynamical Hartree-Fock-Bogoliubov Theory of Vortices in Bose-Einstein Condensates at Finite Temperature

We present a method utilizing the continuity equation for the condensate density to make predictions of the precessional frequency of single off-axis vortices and of vortex arrays in Bose-Einstein condensates at finite temperature. We also present an orthogonalized Hartree-Fock-Bogoliubov (HFB) formalism. We solve the continuity equation for the condensate density self-consistently with the orthogonalized HFB equations, and find stationary solutions in the frame rotating at this frequency. As an example of the utility of this formalism we obtain time-independent solutions for quasi-two-dimensional rotating systems in the co-rotating frame. We compare these results with time-dependent predictions where we simulate stirring of the condensate.Comment: 13 pages, 11 figures, 1 tabl