This article includes a list of general references, but it lacks sufficient corresponding inline citations. Please help to improve this article by introducing more precise citations.(June 2020) (Learn how and when to remove this message)
Median of Medians
Median of medians
Class
Selection algorithm
Data structure
Array
Worst-case performance
Best-case performance
Worst-case space complexity
auxiliary
Optimal
Yes
In computer science, the median of medians is an approximate median selection algorithm, frequently used to supply a good pivot for an exact selection algorithm, most commonly quickselect, that selects the kth smallest element of an initially unsorted array. Median of medians finds an approximate median in linear time. Using this approximate median as an improved pivot, the worst-case complexity of quickselect reduces from quadratic to linear, which is also the asymptotically optimal worst-case complexity of any selection algorithm. In other words, the median of medians is an approximate median-selection algorithm that helps building an asymptotically optimal, exact general selection algorithm (especially in the sense of worst-case complexity), by producing good pivot elements.
Median of medians can also be used as a pivot strategy in quicksort, yielding an optimal algorithm, with worst-case complexity .[citation needed] Although this approach optimizes the asymptotic worst-case complexity quite well, it is typically outperformed in practice by instead choosing random pivots for its average complexity for selection and average complexity for sorting, without any overhead of computing the pivot.
Similarly, Median of medians is used in the hybrid introselect algorithm as a fallback for pivot selection at each iteration until kth smallest is found. This again ensures a worst-case linear performance, in addition to average-case linear performance: introselect starts with quickselect (with random pivot, default), to obtain good average performance, and then falls back to modified quickselect with pivot obtained from median of medians if the progress is too slow. Even though asymptotically similar, such a hybrid algorithm will have a lower complexity than a straightforward introselect up to a constant factor (both in average-case and worst-case), at any finite length.
The algorithm was published in Blum et al. (1973), and thus is sometimes called BFPRT after the last names of the authors. In the original paper the algorithm was referred to as PICK, referring to quickselect as "FIND".
In computer science, the medianofmedians is an approximate median selection algorithm, frequently used to supply a good pivot for an exact selection...
§ Inequality relating means and medians below. As a median is based on the middle data in a set, it is not necessary to know the value of extreme results in order...
Whether in reference to the anatomy of the human or other members of the Bilateria, the median plane, also called a mid-sagittal plane and related terms...
medianof the absolute deviations from the data's median X ~ = median ( X ) {\displaystyle {\tilde {X}}=\operatorname {median} (X)} : MAD = median ...
The median nerve is a nerve in humans and other animals in the upper limb. It is one of the five main nerves originating from the brachial plexus. The...
Furthermore, some types of signals (very often the case for images) use whole number representations: in these cases, histogram medians can be far more efficient...
differ from the mean (or average) income. Both of these are ways of understanding income distribution. Median income can be calculated by household income...
ideal to take the mean of these weighted medians when it makes sense instead. Coincidentally, both the weighted median and median are equal to 2.5, but...
problems of finding the minimum, median, and maximum element in the collection. Selection algorithms include quickselect, and the medianofmedians algorithm...
medians than are feasible with a planted strip, but research indicates that such narrow medians may have minimal safety benefit compared to no median...
The median eminence is generally defined as the portion of the ventral hypothalamus from which the portal vessels arise. The median eminence is a small...
scholarship tends to be skeptical about the existence of a united Median "kingdom" or "state", at least for most of the 7th century BCE. According to classical...
Median regression may refer to: Quantile regression, a regression analysis used to estimate conditional quantiles such as the median Repeated median regression...
The median aperture (also known as the medial aperture and foramen of Magendie) is an opening of the fourth ventricle at the caudal portion of the roof...
This article is a list of countries by median age. The median age is the index that divides the entire population into two numerically equal age groups...
the "Medians"; in fact for a Greek to become "too closely associated with Iranian culture" was "to become Medianized, not Persianized". The Median kingdom...
Median (also Medean or Medic) was the language of the Medes. It is an ancient Iranian language and classified as belonging to the Northwestern Iranian...
In human anatomy, the median cubital vein (or median basilic vein) is a superficial vein of the arm on the anterior aspect of the elbow. It classically...
The palmar branch of the median nerve is a branch of the median nerve which arises at the distal part of the forearm. It pierces the palmar carpal ligament...
rejection was caused only by the shift in medians. It is easy to prove by simulations, where samples with equal medians, yet different scales and shapes, lead...
Coombs' method – satisfy the median voter property in spaces of any dimension for voter distributions with omnidirectional medians. It is easy to construct...
The median arcuate ligament is a ligament under the diaphragm that connects the right and left crura of diaphragm. The median arcuate ligament is formed...
In geometry, the geometric medianof a discrete set of sample points in a Euclidean space is the point minimizing the sum of distances to the sample points...
Median sternotomy is a type of surgical procedure in which a vertical inline incision is made along the sternum, after which the sternum itself is divided...
The median tongue bud (also tuberculum impar) marks the beginning of the development of the tongue. It appears as a midline swelling from the first pharyngeal...
Median rhomboid glossitis is a condition characterized by an area of redness and loss of lingual papillae on the central dorsum of the tongue, sometimes...
Global Information
