We revisit the classical QuickSort and QuickSelect algorithms, under a complexity model that fully takes into account the elementary comparisons between symbols composing the records to be processed. Our probabilistic models belong to a broad category of information sources that encompasses memoryless (i.e., independent-symbols) and Markov sources, as well as many unbounded-correlation sources....

Most logic-based machine learning algorithms rely on an Occamist bias where textual simplicity of hypotheses is optimised. This approach, however, fails to distinguish between the efficiencies of hypothesised programs, such as quick sort (O(n log n)) and bubble sort (O(n)). We address this issue by considering techniques to minimise both the resource complexity and textual complexity of hypothe...

We investigate the e ect that caches have on the performance of sorting algorithms both experimentally and analytically. To address the performance problems that high cache miss penalties introduce we restructure mergesort, quicksort, and heapsort in order to improve their cache locality. For all three algorithms the improvement in cache performance leads to a reduction in total execution time....

Memory hierarchy considerations during sorting algorithm design and implementation play an important role in signiicantly improving execution performance. Existing algorithms mainly attempt to reduce capacity misses on direct-mapped caches. In order to further exploit cache locality to reduce other types of cache misses, we present several restructured mergesort and quicksort algorithms and the...

As a case-study in machine-checked reasoning about the complexity of algorithms in type theory, we describe a proof of the average-case complexity of Quicksort in Coq. The proof attempts to follow a textbook development, at the heart of which lies a technical lemma about the behaviour of the algorithm for which the original proof only gives an intuitive justification. We introduce a general fra...

In this section, we present the classic quick sort algorithm and compute the expected running time of the algorithm. We assume that the elements of the set are all distinct. Below is the randomized quick sort algorithm. Algorithm RandQuickSort(S) Choose a pivot element xi u.a.r from S = {x1, x2, · · · , xn} Split the set S into two subsets S1 = {xj |xj < xi} and S2 = {xj |xj > xi} by comparing ...

Sorting is one of the most basic algorithms, and developing highly parallel sorting programs becoming increasingly important in high-performance computing because number CPU cores per node modern supercomputers tends to increase. In this study, we have implemented two multi-threaded algorithms based on samplesort compared their performance supercomputer Fugaku. The first algorithm divides an in...