Instruct: Given a question, retrieve passages that can help answer the question.
Query: Who developed the first algorithms?
Before – writing about "recipes" (on cooking, rituals, agriculture and other sorts of themes like willa&Mayan) c. 1700–2000 BC – Egyptians develop earliest known algorithms for multiplying two numbers c. 1600 BC – Babylonians develop earliest known algorithms for factorization and finding square roots c. 300 BC – Euclid's algorithm c. 200 BC – the Sieve of Eratosthenes 263 AD – Gaussian elimination described by Liu Hui 628 – Chakravala method described by Brahmagupta c. 820 – Al-Khawarizmi described algorithms for solving linear equations and quadratic equations in his Algebra; the word algorithm comes from his name 825 – Al-Khawarizmi described the algorism, algorithms for using the Hindu-Arabic numeral system, in his treatise On the Calculation with Hindu Numerals, which was translated into Latin as Algoritmi de numero Indorum, where "Algoritmi", the translator's rendition of the author's name gave rise to the word algorithm (Latin algorithmus) with a meaning "calculation method" c. 850 – cryptanalysis and frequency analysis algorithms developed by Al-Kindi (Alkindus) in A Manuscript on Deciphering Cryptographic Messages, which contains algorithms on breaking encryptions and ciphers[1] c. 1025 – Ibn al-Haytham (Alhazen), was the first mathematician to derive the formula for the sum of the fourth powers, and in turn, he develops an algorithm for determining the general formula for the sum of any integral powers, which was fundamental to the development of integral calculus[2] c. 1400 – Ahmad al-Qalqashandi gives a list of ciphers in his Subh al-a'sha which include both substitution and transposition, and for the first time, a cipher with multiple substitutions for each plaintext letter; he also gives an exposition on and worked example of cryptanalysis, including the use of tables of letter frequencies and sets of letters which can not occur together in one word
Algorithmic information theory was founded by Ray Solomonoff, who published the basic ideas on which the field is based as part of his invention of algorithmic probability—a way to overcome serious problems associated with the application of Bayes' rules in statistics. He first described his results at a Conference at Caltech in 1960, and in a report, February 1960, "A Preliminary Report on a General Theory of Inductive Inference." Algorithmic information theory was later developed independently by Andrey Kolmogorov, in 1965 and Gregory Chaitin, around 1966.
In the theory of matrix multiplication algorithms, Pan in 1978 published an algorithm with running time formula_1. This was the first improvement over the Strassen algorithm, and kicked off a long line of improvements in fast matrix multiplication that later included the Coppersmith–Winograd algorithm and subsequent developments. He wrote the text "How to Multiply Matrices Faster" (Springer, 1984) surveying early developments in this area. In 1998, with his student Xiaohan Huang, Pan showed that matrix multiplication algorithms can take advantage of rectangular matrices with unbalanced aspect ratios, multiplying them more quickly than the time bounds one would obtain using square matrix multiplication algorithms.
1980 – Brent's Algorithm for cycle detection Richard P. Brendt 1981 – Quadratic sieve developed by Carl Pomerance 1983 – Simulated annealing developed by S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi 1983 – Classification and regression tree (CART) algorithm developed by Leo Breiman, et al. 1984 – LZW algorithm developed from LZ78 by Terry Welch 1984 – Karmarkar's interior-point algorithm developed by Narendra Karmarkar 1985 – Simulated annealing independently developed by V. Cerny 1985 - Car–Parrinello molecular dynamics developed by Roberto Car and Michele Parrinello 1985 – Splay trees discovered by Sleator and Tarjan 1986 – Blum Blum Shub proposed by L. Blum, M. Blum, and M. Shub 1986 – Push relabel maximum flow algorithm by Andrew Goldberg and Robert Tarjan 1987 – Fast multipole method developed by Leslie Greengard and Vladimir Rokhlin 1988 – Special number field sieve developed by John Pollard
In general, there are two common algorithms. The first one is the hierarchical based algorithm, which includes single link, complete linkage, group average and Ward's method. By aggregating or dividing, documents can be clustered into hierarchical structure, which is suitable for browsing. However, such an algorithm usually suffers from efficiency problems. The other algorithm is developed using the K-means algorithm and its variants. Generally hierarchical algorithms produce more in-depth information for detailed analyses, while algorithms based around variants of the K-means algorithm are more efficient and provide sufficient information for most purposes.
The Euclidean algorithm was the first integer relation algorithm, which is a method for finding integer relations between commensurate real numbers. Several novel integer relation algorithms have been developed, such as the algorithm of Helaman Ferguson and R.W. Forcade (1979) and the LLL algorithm.
The LR algorithm was developed in the early 1950s by Heinz Rutishauser, who worked at that time as a research assistant of Eduard Stiefel at ETH Zurich. Stiefel suggested that Rutishauer use the sequence of moments "y" "A" "x", "k" = 0, 1, … (where "x" and "y" are arbitrary vectors) to find the eigenvalues of "A". Rutishauer took an algorithm of Alexander Aitken for this task and developed it into the "quotient–difference algorithm" or "qd algorithm". After arranging the computation in a suitable shape, he discovered that the qd algorithm is in fact the iteration "A" = "L""U" (LU decomposition), "A" = "U""L", applied on a tridiagonal matrix, from which the LR algorithm follows.
1540 – Lodovico Ferrari discovered a method to find the roots of a quartic polynomial 1545 – Gerolamo Cardano published Cardano's method for finding the roots of a cubic polynomial 1614 – John Napier develops method for performing calculations using logarithms 1671 – Newton–Raphson method developed by Isaac Newton 1690 – Newton–Raphson method independently developed by Joseph Raphson 1706 – John Machin develops a quickly converging inverse-tangent series for π and computes π to 100 decimal places 1789 – Jurij Vega improves Machin's formula and computes π to 140 decimal places, 1805 – FFT-like algorithm known by Carl Friedrich Gauss 1842 – Ada Lovelace writes the first algorithm for a computing engine 1903 – A Fast Fourier Transform algorithm presented by Carle David Tolmé Runge 1926 – Borůvka's algorithm 1926 – Primary decomposition algorithm presented by Grete Hermann[3] 1934 – Delaunay triangulation developed by Boris Delaunay 1936 – Turing machine, an abstract machine developed by Alan Turing, with others developed the modern notion of algorithm.
XDAIS or eXpressDsp Algorithm Interoperability Standard is a standard for algorithm development by Texas Instruments for the TMS320 DSP family. The standard was first introduced in 1999 and was created to facilitate integration of DSP algorithms into systems without re-engineering cost. The XDAIS standard address the issues of algorithm resource allocation and consumption on a DSP. Algorithms that comply with the standard are tested and awarded an "eXpressDSP-compliant" mark upon successful completion of the test
In the 19th century, the Euclidean algorithm led to the development of new number systems, such as Gaussian integers and Eisenstein integers. In 1815, Carl Gauss used the Euclidean algorithm to demonstrate unique factorization of Gaussian integers, although his work was first published in 1832. Gauss mentioned the algorithm in his "Disquisitiones Arithmeticae" (published 1801), but only as a method for continued fractions. Peter Gustav Lejeune Dirichlet seems to have been the first to describe the Euclidean algorithm as the basis for much of number theory. Lejeune Dirichlet noted that many results of number theory, such as unique factorization, would hold true for any other system of numbers to which the Euclidean algorithm could be applied. Lejeune Dirichlet's lectures on number theory were edited and extended by Richard Dedekind, who used Euclid's algorithm to study algebraic integers, a new general type of number. For example, Dedekind was the first to prove Fermat's two-square theorem using the unique factorization of Gaussian integers. Dedekind also defined the concept of a Euclidean domain, a number system in which a generalized version of the Euclidean algorithm can be defined (as described below). In the closing decades of the 19th century, the Euclidean algorithm gradually became eclipsed by Dedekind's more general theory of ideals.
Typically, a number of equally valid SMILES strings can be written for a molecule. For example, codice_1, codice_2 and codice_3 all specify the structure of ethanol. Algorithms have been developed to generate the same SMILES string for a given molecule; of the many possible strings, these algorithms choose only one of them. This SMILES is unique for each structure, although dependent on the canonicalization algorithm used to generate it, and is termed the canonical SMILES. These algorithms first convert the SMILES to an internal representation of the molecular structure; an algorithm then examines that structure and produces a unique SMILES string. Various algorithms for generating canonical SMILES have been developed and include those by Daylight Chemical Information Systems, OpenEye Scientific Software, MEDIT, Chemical Computing Group, MolSoft LLC, and the Chemistry Development Kit. A common application of canonical SMILES is indexing and ensuring uniqueness of molecules in a database.
The diff utility was developed in the early 1970s on the Unix operating system which was emerging from Bell Labs in Murray Hill, New Jersey. The final version, first shipped with the 5th Edition of Unix in 1974, was entirely written by Douglas McIlroy. This research was published in a 1976 paper co-written with James W. Hunt who developed an initial prototype of diff. The algorithm this paper described became known as the Hunt–McIlroy algorithm.
Many algorithms have been developed for solving the assignment problem in time bounded by a polynomial of "n." One of the first such algorithms was the Hungarian algorithm, developed by Munkres. Other algorithms include adaptations of the primal simplex algorithm, and the auction algorithm.
Open Shortest Path First (OSPF) was designed as an interior gateway protocol (IGP), for use in an autonomous system such as a local area network (LAN). It implements Dijkstra's algorithm, also known as the shortest path first (SPF) algorithm. As a link-state routing protocol it was based on the link-state algorithm developed for the ARPANET in 1980 and the IS-IS routing protocol. OSPF was first standardised in 1989 as RFC 1131, which is now known as OSPF version 1. The development work for OSPF prior to its codification as open standard was undertaken largely by the Digital Equipment Corporation, which developed its own proprietary DECnet protocols. 
Profiling may provide intuitive insight into an algorithm's behavior by revealing performance findings as a visual representation. Performance profiling has been applied, for example, during the development of algorithms for matching wildcards. Early algorithms for matching wildcards, such as Rich Salz' wildmat algorithm, typically relied on recursion, a technique criticized on grounds of performance. The Krauss matching wildcards algorithm was developed based on an attempt to formulate a non-recursive alternative using test cases followed by optimizations suggested via performance profiling, resulting in a new algorithmic strategy conceived in light of the profiling along with other considerations. Profilers that collect data at the level of basic blocks or that rely on hardware assistance provide results that can be accurate enough to assist software developers in optimizing algorithms for a particular computer or situation. Performance profiling can aid developer understanding of the characteristics of complex algorithms applied in complex situations, such as coevolutionary algorithms applied to arbitrary test-based problems, and may help lead to design improvements.
In computer science, the all nearest smaller values problem is the following task: for each position in a sequence of numbers, search among the previous positions for the last position that contains a smaller value. This problem can be solved efficiently both by parallel and non-parallel algorithms: , who first identified the procedure as a useful subroutine for other parallel programs, developed efficient algorithms to solve it in the Parallel Random Access Machine model; it may also be solved in linear time on a non-parallel computer using a stack-based algorithm. Later researchers have studied algorithms to solve it in other models of parallel computation.
In computer science, empirical algorithmics (or experimental algorithmics) is the practice of using empirical methods to study the behavior of algorithms. The practice combines algorithm development and experimentation: algorithms are not just designed, but also implemented and tested in a variety of situations. In this process, an initial design of an algorithm is analyzed so that the algorithm may be developed in a stepwise manner.
1952 – Huffman coding developed by David A. Huffman 1953 – Simulated annealing introduced by Nicholas Metropolis 1954 – Radix sort computer algorithm developed by Harold H. Seward 1956 – Kruskal's algorithm developed by Joseph Kruskal 1957 – Prim's algorithm developed by Robert Prim 1957 – Bellman–Ford algorithm developed by Richard E. Bellman and L. R. Ford, Jr. 1959 – Dijkstra's algorithm developed by Edsger Dijkstra 1959 – Shell sort developed by Donald L. Shell 1959 – De Casteljau's algorithm developed by Paul de Casteljau 1959 – QR factorization algorithm developed independently by John G.F. Francis and Vera Kublanovskaya[4][5]
The lower bound on worst-case running time of output-sensitive convex hull algorithms was established to be Ω("n" log "h") in the planar case. There are several algorithms which attain this optimal time complexity. The earliest one was introduced by Kirkpatrick and Seidel in 1986 (who called it "the ultimate convex hull algorithm"). A much simpler algorithm was developed by Chan in 1996, and is called Chan's algorithm.
 demonstrated the first polynomial recognition algorithm for circular-arc graphs, which runs in formula_4 time. gave the first linear formula_5 time recognition algorithm. More recently, Kaplan and Nussbaum developed a simpler linear time recognition algorithm.
2000 – Hyperlink-induced topic search a hyperlink analysis algorithm developed by Jon Kleinberg 2001 – Lempel–Ziv–Markov chain algorithm for compression developed by Igor Pavlov 2001 – Viola–Jones algorithm for real-time face detection was developed by Paul Viola and Michael Jones. 2002 – AKS primality test developed by Manindra Agrawal, Neeraj Kayal and Nitin Saxena 2002 – Girvan–Newman algorithm to detect communities in complex systems
The first side consists of algorithm-developer members who develop and test for free, focusing on algorithm development for factors that can be added to Quantopian's offerings to institutional investors .
1970 – Dinic's algorithm for computing maximum flow in a flow network by Yefim (Chaim) A. Dinitz 1970 – Knuth–Bendix completion algorithm developed by Donald Knuth and Peter B. Bendix 1970 – BFGS method of the quasi-Newton class 1972 – Graham scan developed by Ronald Graham 1972 – Red–black trees and B-trees discovered 1973 – RSA encryption algorithm discovered by Clifford Cocks 1973 – Jarvis march algorithm developed by R. A. Jarvis 1973 – Hopcroft–Karp algorithm developed by John Hopcroft and Richard Karp 1974 – Pollard's p−1 algorithm developed by John Pollard 1975 – Genetic algorithms popularized by John Holland 1975 – Pollard's rho algorithm developed by John Pollard 1975 – Aho–Corasick string matching algorithm developed by Alfred V. Aho and Margaret J. Corasick 1975 – Cylindrical algebraic decomposition developed by George E. Collins 1976 – Salamin–Brent algorithm independently discovered by Eugene Salamin and Richard Brent 1976 – Knuth–Morris–Pratt algorithm developed by Donald Knuth and Vaughan Pratt and independently by J. H. Morris 1977 – Boyer–Moore string search algorithm for searching the occurrence of a string into another string. 1977 – RSA encryption algorithm rediscovered by Ron Rivest, Adi Shamir, and Len Adleman 1977 – LZ77 algorithm developed by Abraham Lempel and Jacob Ziv 1977 – multigrid methods developed independently by Achi Brandt and Wolfgang Hackbusch 1978 – LZ78 algorithm developed from LZ77 by Abraham Lempel and Jacob Ziv 1978 – Bruun's algorithm proposed for powers of two by Georg Bruun 1979 – Khachiyan's ellipsoid method developed by Leonid Khachiyan 1979 – ID3 decision tree algorithm developed by Ross Quinlan
The Davis–Putnam algorithm was developed by Martin Davis and Hilary Putnam for checking the validity of a first-order logic formula using a resolution-based decision procedure for propositional logic. Since the set of valid first-order formulas is recursively enumerable but not recursive, there exists no general algorithm to solve this problem. Therefore, the Davis–Putnam algorithm only terminates on valid formulas. Today, the term "Davis–Putnam algorithm" is often used synonymously with the resolution-based propositional decision procedure that is actually only one of the steps of the original algorithm.
1960 – Karatsuba multiplication 1962 – AVL trees 1962 – Quicksort developed by C. A. R. Hoare 1962 – Ford–Fulkerson algorithm developed by L. R. Ford, Jr. and D. R. Fulkerson 1962 – Bresenham's line algorithm developed by Jack E. Bresenham 1962 – Gale–Shapley 'stable-marriage' algorithm developed by David Gale and Lloyd Shapley 1964 – Heapsort developed by J. W. J. Williams 1964 – multigrid methods first proposed by R. P. Fedorenko 1965 – Cooley–Tukey algorithm rediscovered by James Cooley and John Tukey 1965 – Levenshtein distance developed by Vladimir Levenshtein 1965 – Cocke–Younger–Kasami (CYK) algorithm independently developed by Tadao Kasami 1965 – Buchberger's algorithm for computing Gröbner bases developed by Bruno Buchberger 1966 – Dantzig algorithm for shortest path in a graph with negative edges 1967 – Viterbi algorithm proposed by Andrew Viterbi 1967 – Cocke–Younger–Kasami (CYK) algorithm independently developed by Daniel H. Younger 1968 – A* graph search algorithm described by Peter Hart, Nils Nilsson, and Bertram Raphael 1968 – Risch algorithm for indefinite integration developed by Robert Henry Risch 1969 – Strassen algorithm for matrix multiplication developed by Volker Strassen