There are many randomized “divide and conquer” algorithms, such as randomized Quicksort, whose operation involves partitioning a problem of size n uniformly at random into two subproblems of size k and n − k that are solved recursively. We present a simple combinatorial method for analyzing the expected running time of such algorithms, and prove that under very weak assumptions this expected ru...

7 A Sketch of a Research Immersion Lab/Master Thesis: Randomized Algorithms with Limited Randomness 7 7.1 Experimental Work: Quicksort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 7.2 Experimental Work: Randomized Incremental Constructions . . . . . . . . . . . . . . . . 7 7.3 Theoretical Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

Recently, Phiangsungnoen et al. [J. Inequal. Appl. 2014:201 (2014)] studied fuzzy mappings in the framework of Hausdorff fuzzy metric spaces. Following this direction of research, we establish the existence of fixed fuzzy points of fuzzy mappings. An example is given to support the result proved herein; we also present a coincidence and common fuzzy point result. Finally, as an application of o...

The introduction of the PowerPC 970 JS20 blade server opens opportunities for vectorizing commercial applications using the integrated AltiVec unit. We examined the vectorization of applications from diverse fields such as XML parsing, UTF-8 encoding, life sciences, string manipulations, and sorting. We obtained performance speedups (over optimized scalar code) for string comparisons (2-3), XML...

Algorithms for crowdsourced tasks such as entity resolution, sorting, etc. have been subject to a variety of research work. So far, all of this work has focused on one specific problem respectively. In this paper, we want to focus on the bigger picture. More specifically, we want to show how it is possible to estimate the budget or the quality of an algorithm in a crowdsourcing environment wher...

Sundararajan and Chakraborty [10] introduced a new version of Quick sort removing the interchanges. Khreisat [1] found this algorithm to be competing well with some other versions of Quick sort. However, it uses an auxiliary array thereby increasing the space complexity. Here, we provide a second version of our new sort where we have removed the auxiliary array. This second improved version of ...

We describe a general framework for realistic analysis of sorting and searching algorithms, and we apply it to the average-case analysis of five basic algorithms: three sorting algorithms (QuickSort, InsertionSort, BubbleSort) and two selection algorithms (QuickMin and SelectionMin). Usually, the analysis deals with the mean number of key comparisons, but, here, we view keys as words produced b...

The multiple selection problem asks for the elements of rank r1, r2, . . . , rk from a linearly ordered set of n elements. Let B denote the information theoretic lower bound on the number of element comparisons needed for multiple selection. We first show that a variant of multiple quickselect — a well known, simple, and practical generalization of quicksort — solves this problem with B + O(n) ...

QuickSort Hoare [1962] (A) Pick a pivot element from array (B) Split array into 3 subarrays: those smaller than pivot, those larger than pivot, and the pivot itself. (C) Recursively sort the subarrays, and concatenate them. Randomized QuickSort (A) Pick a pivot element uniformly at random from the array (B) Split array into 3 subarrays: those smaller than pivot, those larger than pivot, and the...

Efficient index construction in multidimensional data spaces is important for many knowledge discovery algorithms, because construction times typically must be amortized by performance gains in query processing. In this paper, we propose a generic bulk loading method which allows the application of user-defined split strategies in the index construction. This approach allows the adaptation of t...