Distributional convergence for the number of symbol comparisons used by QuickSelect

When the search algorithm QuickSelect compares keys during its execution in order to find a key of target rank, it must operate on the keys' representations or internal structures, which were ignored by the previous studies that quantified the execution cost for the algorithm in terms of the number of required key comparisons. In this paper, we analyze running costs for the algorithm that take into account not only the number of key comparisons but also the cost of each key comparison. We suppose that keys are represented as sequences of symbols generated by various probabilistic sources and that QuickSelect operates on individual symbols in order to find the target key. We identify limiting distributions for the costs and derive integral and series expressions for the expectations of the limiting distributions. These expressions are used to recapture previously obtained results on the number of key comparisons required by the algorithm.Comment: The first paragraph in the proof of Theorem 3.1 has been corrected in this revision, and references have been update

Arithmetic and Distance-Based Approach to the Statistical Analysis of Imprecisely Valued Data

Most of the research developed in the last years by the SMIRE Research Group concerns the statistical analysis of imprecisely (set- and fuzzy set)-valued experimental data. This analysis has been based on an approach considering the usual arithmetic for these data as well as suitable metrics between them. The research perfectly fits into the research directions of the COST Action IC0702, which has been particularly helpful for scientific activities, discussions and exchanges associated with group members. The main objective of this paper is to summarize some of the main recent advances of the SMIRE Research Group. © Springer-Verlag 2013