For many geometric problems, there are ecient algorithms that surprisingly use very little extra space other than the given array holding the input. For many geometric query problems, there are ecient data structures that need no extra space at all other than an array holding a permutation of the input. In this paper, we obtain the rst such space-economical solutions for a number of fundamental problems, including three-dimensional convex hulls, two-dimensional Delaunay triangulations, xed-dimensional range queries, and xed-dimensional nearest neighbor queries.

Quicksort was first introduced in 1961 by Hoare. Many variants have been developed, the best of which are among the fastest generic sorting algorithms available, as testified by the choice of Quicksort as the default sorting algorithm in most programming libraries. Some sorting algorithms are adaptive, i.e. they have a complexity analysis which is better for inputs which are nearly sorted, according to some specified measure of presortedness. Quicksort is not among these, as it uses Ω(n log n) comparisons even when the input is already sorted. However, in this paper we demonstrate empirically that the actual running time of Quicksort is adaptive with respect to the presortedness measure Inv. Differences close to a factor of two are observed between instances with low and high Inv value. We then show that for the randomized version of Quicksort, the number of element swaps performed is provably adaptive with respect to the measure Inv. More precisely, we prove that randomized Quicksort performs expected O(n(1+log(1+ Inv/n))) element swaps, where Inv denotes the number of inversions in the input sequence. This result provides a theoretical explanation for the observed behavior, and gives new insights on the behavior of the Quicksort algorithm. We also give some empirical results on the adaptive behavior of Heapsort and Mergesort.

Traditionally, the field of scientific computing has been dominated by numerical methods. However, modern scientific codes often combine numerical methods with combinatorial methods. Sorting, a widely studied problem in computer science, is an important primitive for combinatorial scientific computing. As high

Abstract — One of the most frequent operation performed on database is searching. To perform this operation we have different kinds of searching algorithms, some of which are Binary Search, Index Sequential Access Method (ISAM), but these and all other searching algorithms work only on data, which are previously sorted. An efficient algorithm is required in order to make the searching algorithm fast and efficient. This research paper presents a new sorting algorithm named as “Optimized Selection Sort Algorithm, OSSA”.OSSA is designed to perform sorting quickly and more effectively as compared to the existing version of selection sort. The introduction of OSSA version of selection sort algorithm for sorting the data stored in database instead of existing selection sort algorithm will provide an opportunity to the users to save almost 50 % of their operation time with almost 100% accuracy.

ABSTRACT – Optimized Selection Sort Algorithm is a new sorting algorithm that has been developed to address the shortcomings of the current popular sorting algorithms. The goal of this research is to perform an extensive empirical analysis of Optimized Selection Sort against Selection Sort and Insertion Sort Algorithms. The results proved that Optimized Selection Sort is much more efficient than Selection Sort Algorithm; Furthermore analysis supports the fact that Optimized Selection Sort is better than Insertion Sort