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An algorithm is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and automated reasoning in mathematics and computer science. An algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Starting from an first state and first input the instructions describe a computation when executed proceeds through a finite number of well-defined successive states eventually producing "output" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic some algorithms known as randomized algorithms incorporate random input. An algorithm is a procedure or formula for solving a problem. The word derives from the name of the mathematician Al-Khwarizmi's work is the likely source for the word algebra as well. A computer program can be viewed as an elaborate algorithm. In mathematics and computer science, an algorithm usually means a small procedure that solves a recurrent problem. An informal definition could be "a set of rules that precisely defines a sequence of operations." which would include all computer programs, including programs that do not perform numeric calculations. Generally, a program is only an algorithm if it stops eventually. A prototypical example of an algorithm is Euclid's algorithm to determine the maximum common divisor of two integers; an example (there are others) is described by the flow chart above and as an example in a later section. Algorithms are essential to the way computers process data.
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Scope and Importance
Many computer programs contain algorithms that detail the specific instructions a computer should perform (in a specific order) to carry out a specified task, such as calculating employees' paychecks or printing students' report cards. Thus, an algorithm can be considered to be any sequence of operations that can be simulated by a Turing-complete system. Typically, when an algorithm is associated with processing information, data is read from an input source, written to an output device, and/or stored for further processing. Stored data is regarded as part of the internal state of the entity performing the algorithm. In practice, the state is stored in one or more data structures. For some such computational process, the algorithm must be rigorously defined: specified in the way it applies in all possible circumstances that could arise. That is, any conditional steps must be systematically dealt with, case-by-case; the criteria for each case must be clear (and computable). Because an algorithm is a precise list of precise steps, the order of computation is always critical to the functioning of the algorithm. Instructions are usually assumed to be listed explicitly, and are described as starting "from the top" and going "down to the bottom" described as flow of control. The formalization of an algorithm has assumed the premises of imperative programming. This is the most common conception and it attempts to describe a task in discrete "mechanical" means. Unique to this conception of formalized algorithms is the assignment operation, setting the value of a variable. It derives from the intuition of "memory" as a scratchpad. 'Algorithm' stems from the name of a Latin translation of a book written by al-Khwārizmī, a Persian mathematician, astronomer and geographer. Al-Khwarizmi wrote a book titled On the Calculation with Hindu Numerals in about 825 AD, and was principally responsible for spreading the Indian system of numeration throughout the Middle East and Europe. It was translated into Latin as Algoritmi de numero Indorum. The term "Algoritmi" in the title of the book led to the term "algorithm".
The market for Algebra is expected to grow at a significant during the forecast period from 2014 to 2020 owing to increasing Computer science and engineering and in Mathematics. The global algorithm market is estimated to currently be worth $1.3 billion, and is forecast to reach a value of $1.6 billion by 2017.
Discrete Algorithms (SODA16)
January 10-12, 2016, Arlington, Virginia
Algorithms and Discrete Applied Mathematics,
February 18-20, 2016, Thiruvanthapuram, IndiaALEA 2016.
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This page was last updated on July 31, 2021