We revisit the method of Kirschenhofer, Prodinger and Tichy to calculate the moments of number of comparisons used by the randomized quick sort algorithm. We reemphasize that this approach helps in calculating these quantities with less computation. We also point out that as observed by Knuth this method also gives moments for total path length of a binary search tree built over a random set of...

This paper addresses the problem of using functional programming on a SIMD or data parallel architecture. Each type of operation the architecture can perform corresponds to a particular function application. Therefore it is possible to write low level data parallel algorithms directly in a functional language. This has two advantages: the low level algorithms are easier to derive, and the full ...

Sorting sets of numbers is usually considered in the context of a software algorithm. However, when sorting functionality needs to be implemented in hardware, adapting a known sorting algorithm into hardware (i.e. quicksort, mergesort, etc.) may not be the most e cient or straightforward method. This is especially true when sorting relatively small sets of numbers, for example sets with 32 or f...

We present a new adaptive sorting algorithm which is optimal for most disorder metrics and, more important, has a simple and quick implementation. On input X, our algorithm has a theoretical Ω(|X|) lower bound and a O(|X| log |X|) upper bound, exhibiting amazing adaptive properties which makes it run closer to its lower bound as disorder (computed on different metrics) diminishes. From a practi...

Random trees are of prime importance for studying the average case behavior of algorithms and data structures. The canonical examples are Hoare’s quicksort algorithm and the binary search tree. The most natural parameter to study is the average running time of the algorithm, and the average time for answering a query in a data structure. This does not provide sufficient information to properly ...

• Las Vegas Algorithms: These refer to the randomized algorithms that always come up with a/the correct answer. Their “expected” running time is polynomial in the size of their input, which means that the average running time over all possible coin tosses is polynomial. In the worst case, however, a Las Vegas algorithm may take exponentially long. One example of a Las Vegas algorithm is Quickso...

Recent works showed that implementations of quicksort using vector CPU instructions can outperform the non-vectorized algorithms in widespread use. However, these are typically single-threaded, implemented for a particular instruction set, and restricted to small set key types. We lift three restrictions: our proposed vqsort algorithm integrates into state-of-the-art parallel sorter i p s 4 o $...

Most previous studies of the sorting algorithm QuickSort have used the number of key comparisons as a measure of the cost of executing the algorithm. Here we suppose that the n independent and identically distributed (iid) keys are each represented as a sequence of symbols from a probabilistic source and that QuickSort operates on individual symbols, and we measure the execution cost as the num...

An algorithm is presented that efficiently solves the selection problem: finding the k-th smallest member of a set. Relevant to a divide-and-conquer strategy, the algorithm also partitions a set into small and large valued subsets. Applied recursively, this partitioning results in a sorted set. The algorithm’s applicability is therefore much broader than just the selection problem. The presente...