In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position of a target value within a sorted array. Binary search compares the target value to the middle element of the array. If they are not equal, the half in which the target cannot lie is eliminated and the search continues on the remaining half, again taking the middle element to compare to the target value, and repeating this until the target value is found. If the search ends with the remaining half being empty, the target is not in the array.
In computer science, merge sort is an efficient, general-purpose, and comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the relative order of equal elements is the same in the input and output. Merge sort is a divide-and-conquer algorithm that was invented by John von Neumann in 1945. A detailed description and analysis of bottom-up merge sort appeared in a report by Goldstine and von Neumann as early as 1948.
Merge algorithms are a family of algorithms that take multiple sorted lists as input and produce a single list as output, containing all the elements of the inputs lists in sorted order. These algorithms are used as subroutines in various sorting algorithms, most famously merge sort.
In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is important for optimizing the efficiency of other algorithms that require input data to be in sorted lists. Sorting is also often useful for canonicalizing data and for producing human-readable output.
In computer science, selection sort is an in-place comparison sorting algorithm. It has an O(n2) time complexity, which makes it inefficient on large lists, and generally performs worse than the similar insertion sort. Selection sort is noted for its simplicity and has performance advantages over more complicated algorithms in certain situations, particularly where auxiliary memory is limited.
A binary heap is a heap data structure that takes the form of a binary tree. Binary heaps are a common way of implementing priority queues. The binary heap was introduced by J. W. J. Williams in 1964, as a data structure for heapsort.
Bucket sort, or bin sort, is a sorting algorithm that works by distributing the elements of an array into a number of buckets. Each bucket is then sorted individually, either using a different sorting algorithm, or by recursively applying the bucket sorting algorithm. It is a distribution sort, a generalization of pigeonhole sort that allows multiple keys per bucket, and is a cousin of radix sort in the most-to-least significant digit flavor. Bucket sort can be implemented with comparisons and therefore can also be considered a comparison sort algorithm. The computational complexity depends on the algorithm used to sort each bucket, the number of buckets to use, and whether the input is uniformly distributed.
Quicksort is an efficient, general-purpose sorting algorithm. Quicksort was developed by British computer scientist Tony Hoare in 1959 and published in 1961. It is still a commonly used algorithm for sorting. Overall, it is slightly faster than merge sort and heapsort for randomized data, particularly on larger distributions.
In statistics, the Kendall rank correlation coefficient, commonly referred to as Kendall's τ coefficient, is a statistic used to measure the ordinal association between two measured quantities. A τ test is a non-parametric hypothesis test for statistical dependence based on the τ coefficient. It is a measure of rank correlation: the similarity of the orderings of the data when ranked by each of the quantities. It is named after Maurice Kendall, who developed it in 1938, though Gustav Fechner had proposed a similar measure in the context of time series in 1897.
Samplesort is a sorting algorithm that is a divide and conquer algorithm often used in parallel processing systems. Conventional divide and conquer sorting algorithms partitions the array into sub-intervals or buckets. The buckets are then sorted individually and then concatenated together. However, if the array is non-uniformly distributed, the performance of these sorting algorithms can be significantly throttled. Samplesort addresses this issue by selecting a sample of size s from the n-element sequence, and determining the range of the buckets by sorting the sample and choosing p−1 < s elements from the result. These elements then divide the array into p approximately equal-sized buckets. Samplesort is described in the 1970 paper, "Samplesort: A Sampling Approach to Minimal Storage Tree Sorting", by W. D. Frazer and A. C. McKellar.
A kinetic data structure is a data structure used to track an attribute of a geometric system that is moving continuously. For example, a kinetic convex hull data structure maintains the convex hull of a group of moving points. The development of kinetic data structures was motivated by computational geometry problems involving physical objects in continuous motion, such as collision or visibility detection in robotics, animation or computer graphics.
A Kinetic Heap is a kinetic data structure, obtained by the kinetization of a heap. It is designed to store elements where the priority is changing as a continuous function of time. As a type of kinetic priority queue, it maintains the maximum priority element stored in it. The kinetic heap data structure works by storing the elements as a tree that satisfies the following heap property – if B is a child node of A, then the priority of the element in A must be higher than the priority of the element in B. This heap property is enforced using certificates along every edge so, like other kinetic data structures, a kinetic heap also contains a priority queue to maintain certificate failure times.
A kinetic convex hull data structure is a kinetic data structure that maintains the convex hull of a set of continuously moving points. It should be distinguished from dynamic convex hull data structures, which handle points undergoing discrete changes such as insertions or deletions of points rather than continuous motion.
A Kinetic Tournament is a kinetic data structure that functions as a priority queue for elements whose priorities change as a continuous function of time. It is implemented analogously to a "tournament" between elements to determine the "winner", with the certificates enforcing the winner of each "match" in the tournament. It supports the usual priority queue operations - insert, delete and find-max. They are often used as components of other kinetic data structures, such as kinetic closest pair.
A kinetic diameter data structure is a kinetic data structure which maintains the diameter of a set of moving points. The diameter of a set of moving points is the maximum distance between any pair of points in the set. In the two dimensional case, the kinetic data structure for kinetic convex hull can be used to construct a kinetic data structure for the diameter of a moving point set that is responsive, compact and efficient.
A Kinetic Heater is a kinetic priority queue similar to a kinetic heap, that makes use of randomization to simplify its analysis in a way similar to a treap. Specifically, each element has a random key associated with it in addition to its priority. The kinetic heater is then simultaneously a binary search tree on the element keys, and a heap on the element priorities. The kinetic heater achieves (expected) asymptotic performance bounds equal to the best kinetic priority queues. In practice however, it is less efficient since the extra random keys need to be stored, and the procedure to handle certificate failure is a rotation instead of a simple swap.
A Kinetic hanger is a randomized version of a kinetic heap whose performance is easy to analyze tightly. A kinetic hanger satisfies the heap property but relaxes the requirement that the tree structure must be strictly balanced, thus insertions and deletions can be randomized. As a result, the structure of the kinetic hanger has the property that it is drawn uniformly at random from the space of all possible heap-like structures on its elements.
A kinetic width data structure is a kinetic data structure which maintains the width of a set of moving points. In 2D, the width of a point set is the minimum distance between two parallel lines that contain the point set in the strip between them. For the two dimensional case, the kinetic data structure for kinetic convex hull can be used to construct a kinetic data structure for the width of a point set that is responsive, compact and efficient.
A kinetic minimum spanning tree is a kinetic data structure that maintains the minimum spanning tree (MST) of a graph whose edge weights are changing as a continuous function of time.
In computer science, the order-maintenance problem involves maintaining a totally ordered set supporting the following operations:
