Smart Sort algorithm is a “smart” fusion of heap construction procedures (of Heap sort algorithm) into the conventional “Partition” function (of Quick sort algorithm) resulting in a robust version of Quick sort algorithm. We have also performed empirical analysis of average case behavior of our proposed algorithm along with the necessary theoretical analysis for best and worst cases. Its perfor...

We establish asymptotic expansions for factorial moments of following distributions: number of cycles in a random permutation, number of inversions in a random permutation, and number of comparisons used by the randomized quick sort algorithm. To achieve this we use singularity analysis of certain type of generating functions due to Flajolet and Odlyzko.

This paper presents two new parallel algorithms QSP1 and QSP2 based on sequential quicksort for sorting data on a mesh multicomputer, and analyzes their scalability using the isoeeciency metric. We show that QSP2 matches the lower bound on the isoee-ciency function for mesh multicomputers. The isoef-ciency of QSP1 is also fairly close to optimal. Lang et al. and Schnorr et al. have developed pa...

This appendix to [2] contains a proof of the improved estimates in Remark 7.3 of that paper for the moment generating function of the (normalized) number of comparisons in Quicksort. AMS 2000 subject classifications. Primary 68W40; secondary 68P10, 60F05, 60E10. Date. May 22, 2001. Research supported by NSF grant DMS–9803780, and by The Johns Hopkins University’s Acheson J. Duncan Fund for the ...

In a continuous-time setting, Fill (2012) proved, for a large class of probabilistic sources, that the number of symbol comparisons used by QuickSort, when centered by subtracting the mean and scaled by dividing by time, has a limiting distribution, but proved little about that limiting random variable Y —not even that it is nondegenerate. We establish the nondegeneracy of Y . The proof is perh...

In this study, we propose an optical character recognition technique using Intro Sort. Main feature of this proposed technique is that we segment images using intro sort. It reduces the comparison time for matching the pixels of an image. It reflects reduction in OCR time. Intro sort algorithm begins with quick sort and when recursion depth exceeds a level it switches to heap sort, based on the...

Textbook coverage of algorithm performance emphasizes patterns of growth in expected and worst case execution times, relative to the size of the problem. Variability in execution times for a given problem size is usually ignored. In this research study, our primary focus is on the empirical distribution of execution times for a given algorithm and problem size. We examine CPU times for Java imp...

We analyse the average-case cache performance of distribution sorting algorithms in the case when keys are independently but not necessarily uniformly distributed. The analysis is for both ‘in-place’ and ‘out-of-place’ distribution sorting algorithms and is more accurate than the analysis presented in [13]. In particular, this new analysis yields tighter upper and lower bounds when the keys are...