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From Wikipedia, the free encyclopedia

The following is a list of algorithms described in Wikipedia. This list is manually updated and additions of links to existing pages are welcome. See also the list of data structures, list of algorithm general topics and list of terms relating to algorithms and data structures.

If you intend to describe a new algorithm, please read algorithms on Wikipedia first, then add a link to your article and a one-line description here.

Contents 1 Abstract Algebra 2 Coding Theory 3 Combinatorial algorithms 3.1 General combinatorial algorithms 3.2 Graph algorithms 3.2.1 Network theory 3.2.2 Routing Problems 3.2.3 Subgraphs 3.3 Search algorithms 3.4 String algorithms 3.4.1 Searching 3.4.2 Approximate matching 3.5 Sorting algorithms 3.6 Merge algorithms 4 Compression algorithms 4.1 Lossless compression algorithms 4.2 Lossy compression algorithms 5 Computational geometry 6 Computer algebra 7 Computer graphics 8 Computer vision 9 Cryptographic algorithms 10 Digital signal processing 10.1 Image Processing 11 Electronics and hardware algorithms 12 Machine Learning and Statistical Classification 13 Number theoretic algorithms 14 Numerical algorithms 14.1 Elementary and Special Functions 14.2 Geometric 14.3 Interpolation and Extrapolation 14.4 Numerical Integration 14.5 Linear Algebra 14.6 Monte Carlo 14.7 Root Finding 15 Optimization algorithms 16 Programming Language Theory 16.1 Parsing 17 Quantum algorithms 18 Science and Medicine 18.1 Astronomy 18.2 Geoscience 18.3 Physics 18.4 Linguistics 18.5 Medicine 19 Software engineering 19.1 Database algorithms 19.2 Distributed systems algorithms 19.3 Memory Allocation and deallocation algorithms 19.4 Operating systems algorithms 19.4.1 Disk scheduling algorithms: 19.4.2 Networking algorithms 19.4.3 Process synchronization algorithms: 19.4.4 Scheduling algorithms 20 Statistical Algorithms 21 Theory of computation and automata 22 Other 23 See also

[edit] Abstract Algebra

• Chien search: a recursive algorithm for determining roots of polynomials defined over a finite field
• Schreier-Sims algorithm: computing a base and strong generating set (BSGS) of a permutation group
• Todd-Coxeter algorithm: Procedure for generating cosets.

[edit] Coding Theory

• Redundancy checks: extra data added to a message for the purposes of error detection
  • Adler-32
  • Cyclic redundancy check
  • Fletcher's checksum
  • Luhn algorithm: a method of validating identification numbers
  • Luhn mod N algorithm: extension of Luhn to non-numeric characters
  • Parity: simple/fast error detection technique
  • Verhoeff algorithm
  • Longitudinal redundancy check (LRC)
• Error detection and correction: detecting and potentially correcting data errors
  • BCH Codes
    • Berlekamp–Massey algorithm
    • Peterson-Gorenstein-Zierler algorithm
    • Reed Solomon error correction
  • BCJR algorithm: decoding of error correcting codes defined on trellises (principally convolutional codes)
  • Hamming codes
    • Hamming(7,4): a Hamming code that encodes 4 bits of data into 7 bits by adding 3 parity bits
• Hamming distance: sum number of positions which are different
• Hamming weight (population count): find the number of 1 bits in a binary word

[edit] Combinatorial algorithms

[edit] General combinatorial algorithms

• Brent's algorithm: finds cycles in iterations using only two iterators
• Floyd's cycle-finding algorithm: finds cycles in iterations
• Gale-Shapley algorithm: solve the stable marriage problem
• Pseudorandom number generators (uniformly distributed):
  • Blum Blum Shub
  • Mersenne twister
  • Linear congruential generator
  • Lagged Fibonacci generator
• Permutations
  • Fisher-Yates shuffle (also known as the Knuth shuffle): randomly shuffle a finite set
  • Robinson–Schensted algorithm: generates permutations from pairs of Young tableaux
  • Steinhaus-Johnson-Trotter algorithm (also known as the Johnson-Trotter algorithm): generate permutations by transposing elements

[edit] Graph algorithms

• Coloring algorithm: Graph coloring algorithm.
• Hopcroft–Karp algorithm: convert a bipartite graph to a maximum cardinality matching
• Hungarian algorithm: algorithm for finding a perfect matching
• Spring based algorithm: algorithm for graph drawing
• Tarjan's off-line least common ancestors algorithm: compute lowest common ancestors for pairs of nodes in a tree
• Topological sort: finds linear order of nodes(e.g. jobs) based on their dependencies.

[edit] Network theory

• Network analysis
  • Link analysis
    • Girvan-Newman algorithm: detect communities in complex systems
    • Web link analysis
      • Hyperlink-Induced Topic Search (HITS) (also known as Hubs and authorities)
      • PageRank
      • TrustRank
• Flow networks
  • Edmonds-Karp algorithm: implementation of Ford-Fulkerson
  • Ford-Fulkerson algorithm: computes the maximum flow in a graph
  • Karger's algorithm: a Monte Carlo method to compute the minimum cut of a connected graph

[edit] Routing Problems

• Edmonds's algorithm (also known as Chu–Liu/Edmonds's algorithm): find maximum or minimum branchings
• Minimum spanning tree
  • Boruvka's algorithm
  • Kruskal's algorithm
  • Prim's algorithm
• Nonblocking Minimal Spanning Switch say, for a telephone exchange
• Shortest path problem
  • Bellman-Ford algorithm: computes shortest paths in a weighted graph (where some of the edge weights may be negative)
  • Dijkstra's algorithm: computes shortest paths in a graph with non-negative edge weights
  • Floyd-Warshall algorithm: solves the all pairs shortest path problem in a weighted, directed graph
  • Johnson algorithm: All pairs shortest path algorithm in sparse weighted directed graph
  • Perturbation methods: an algorithm that computes a locally shortest paths in a graph
• Traveling salesman problem
  • Christofides algorithm
  • Nearest neighbour algorithm

[edit] Subgraphs

• Bron–Kerbosch algorithm: a technique for finding maximal cliques in an undirected graph
• Strongly connected components
  • Cheriyan/Mehlhorn/Gabow algorithm
  • Kosaraju's algorithm
  • Tarjan's algorithm

[edit] Search algorithms

• A* tree search: special case of best-first search that uses heuristics to improve speed
• B* search: a best-first graph search algorithm that finds the least-cost path from a given initial node to any goal node (out of one or more possible goals)
• Backtracking: abandon partial solutions when they are found not to satisfy a complete solution
• Best-first search: traverses a graph in the order of likely importance using a priority queue
• Binary search algorithm: locates an item in a sorted list
• Binary search tree: uses binary tree to maintain elements.
• Breadth-first search: traverses a graph level by level
• Depth-first search: traverses a graph branch by branch
• Hash table: finds an item in an unsorted collection in O(1) time.
• Iterative deepening depth-first search (IDDFS): a state space search strategy
• Linear search: finds an item in an unsorted list
• Predictive search: binary like search which factors in magnitude of search term versus the high and low values in the search. Sometimes called dictionary search or interpolated search.
• Selection algorithm: finds the kth largest item in a list
• Uniform-cost search: a tree search that finds the lowest cost route where costs vary

[edit] String algorithms

[edit] Searching

• Kadane's algorithm: finds maximum sub-array of any size
• Longest common subsequence problem: Find the longest subsequence common to all sequences in a set of sequences
• Longest common substring problem: find the longest string (or strings) that is a substring (or are substrings) of two or more strings
• Longest increasing subsequence problem: find the longest increasing subsequence of a given sequence
• Shortest common supersequence problem: Find the shortest string that contains two or more strings as subsequences
• Substring search
  • Aho-Corasick algorithm: trie based algorithm for finding all substring matches to any of a finite set of strings
  • Boyer-Moore string search algorithm: amortised linear (sublinear in most times) algorithm for substring search
  • Boyer-Moore-Horspool algorithm: Simplification of Boyer-Moore
  • Knuth-Morris-Pratt algorithm: substring search which bypasses reexamination of matched characters
  • Rabin-Karp string search algorithm: searches multiple patterns efficiently
  • Zhu-Takaoka: a variant of the Boyer-Moore string search algorithm

[edit] Approximate matching

• Bitap algorithm: fuzzy algorithm that determines if strings are approximately equal.
• String metrics: compute a similarity or dissimilarity (distance) score between two pairs of text strings
  • Damerau–Levenshtein distance compute a distance measure between two strings, improves on Levenshtein distance
  • Dice's coefficient (also known as the Dice coefficient): a similarity measure related to the Jaccard index
  • Hamming distance: sum number of positions which are different
  • Jaro-Winkler distance: is a measure of similarity between two strings
  • Levenshtein edit distance: compute a metric for the amount of difference between two sequences
• Phonetic algorithms
  • Daitch-Mokotoff Soundex: a Soundex refinement which allows matching of Slavic and Yiddish surnames
  • Double Metaphone: an improvement on Metaphone
  • Metaphone: an algorithm for indexing words by their sound, when pronounced in English
  • NYSIIS: phonetic algorithm, improves on Soundex
  • Soundex: a phonetic algorithm for indexing names by sound, as pronounced in English
• Sequence alignment
  • Hirschberg's algorithm: finds the least cost sequence alignment between two sequences, as measured by their Levenshtein distance
  • Needleman-Wunsch algorithm: find global alignment between two sequences
  • Smith-Waterman algorithm: find local sequence alignment
  • Dynamic time warping: measure similarity between two sequences which may vary in time or speed

[edit] Sorting algorithms

• Exchange Sorts
  • Bubble sort: for each pair of indices, swap the items if out of order
  • Cocktail sort
  • Comb sort
  • Gnome sort
  • Odd-even sort
  • Quicksort: divide list into two, with all items on the first list coming before all items on the second list.; then sort the two lists. Often the method of choice
• Humorous or ineffective
  • Bogosort
  • Stooge sort
• Hybrid
  • Flashsort
  • Introsort: begin with quicksort and switch to heapsort when the recursion depth exceeds a certain level
• Insertion sorts
  • Insertion sort: determine where the current item belongs in the list of sorted ones, and insert it there
  • Library sort
  • Patience sorting
  • Shell sort: an attempt to improve insertion sort
  • Tree sort (binary tree sort): build binary tree, then traverse it to create sorted list
• Merge sorts
  • Merge sort: sort the first and second half of the list separately, then merge the sorted lists
  • Strand sort
• Non-comparison sorts
  • Bead sort
  • Bucket sort
  • Burstsort: build a compact, cache efficient burst trie and then traverse it to create sorted output
  • Counting sort
  • Pigeonhole sort
  • Postman sort: variant of Bucket sort which takes advantage of hierarchical structure
  • Radix sort: sorts strings letter by letter
• Selection sorts
  • Heapsort: convert the list into a heap, keep removing the largest element from the heap and adding it to the end of the list
  • Selection sort: pick the smallest of the remaining elements, add it to the end of the sorted list
  • Smoothsort
• Other
  • Bitonic sorter
  • Pancake sorting
  • Topological sort

[edit] Merge algorithms

• Simple Merge algorithm
• k-way Merge algorithm

[edit] Compression algorithms

[edit] Lossless compression algorithms

• Burrows-Wheeler transform: preprocessing useful for improving lossless compression
• Context tree weighting
• Delta encoding: aid to compression of data in which sequential data occurs frequently
• Dynamic Markov Compression: Compression using predictive arithmetic coding
• Dictionary coders
  • Byte pair encoding (BPE)
  • DEFLATE
  • Lempel-Ziv
    • LZ77 and LZ78
    • Lempel-Ziv Jeff Bonwick (LZJB)
    • Lempel-Ziv-Markov chain-Algorithm (LZMA)
    • Lempel-Ziv-Oberhumer (LZO): speed oriented
    • Lempel-Ziv-Storer-Szymanski (LZSS)
    • Lempel-Ziv-Welch (LZW)
    • LZWL: syllable-based variant
    • LZX
    • Lempel-Ziv Ross Williams (LZRW)
• Entropy encoding: coding scheme that assigns codes to symbols so as to match code lengths with the probabilities of the symbols
  • Arithmetic coding: advanced entropy coding
    • Range encoding: same as arithmetic coding, but looked at in a slightly different way
  • Huffman coding: simple lossless compression taking advantage of relative character frequencies
    • Adaptive Huffman coding: adaptive coding technique based on Huffman coding
    • Package-Merge: Optimizes Huffman coding subject to a length restriction on code strings
  • Shannon-Fano coding
  • Shannon-Fano-Elias coding: precursor to arithmetic encoding[1]
• Entropy coding with known entropy characteristics
  • Golomb coding: form of entropy coding that is optimal for alphabets following geometric distributions
  • Rice coding: form of entropy coding that is optimal for alphabets following geometric distributions
  • Truncated binary encoding
  • Unary coding: code that represents a number n with n ones followed by a zero
  • Universal codes: encodes positive integers into binary code words
    • Elias delta, gamma, and omega coding
    • Exponential-Golomb coding
    • Fibonacci coding
    • Levenshtein coding
• Fast Efficient & Lossless Image Compression System (FELICS): a lossless image compression algorithm
• Incremental encoding: delta encoding applied to sequences of strings
• Prediction by partial matching (PPM): an adaptive statistical data compression technique based on context modeling and prediction
• Run-length encoding: lossless data compression taking advantage of strings of repeated characters
• SEQUITUR algorithm: lossless compression by incremental grammar inference on a string

[edit] Lossy compression algorithms

• 3Dc: a lossy data compression algorithm for normal maps
• Audio and Speech compression
  • A-law algorithm: standard companding algorithm
  • Code excited linear prediction (CELP): low bit-rate speech compression
  • Linear predictive coding (LPC): lossy compression by representing the spectral envelope of a digital signal of speech in compressed form
  • Mu-law algorithm: standard analog signal compression or companding algorithm
  • Warped Linear Predictive Coding (WLPC)
• Image Compression
  • Block Truncation Coding (BTC): a type of lossy image compression technique for greyscale images
  • Embedded Zerotree Wavelet (EZW)
  • Fast Cosine Transform algorithms (FCT algorithms): compute Discrete Cosine Transform (DCT) efficiently
  • Fractal compression: method used to compress images using fractals
  • Set Partitioning in Hierarchical Trees (SPIHT)
  • Wavelet compression: form of data compression well suited for image compression (sometimes also video compression and audio compression)
• Transform coding: type of data compression for "natural" data like audio signals or photographic images
• Vector quantization: technique often used in lossy data compression

[edit] Computational geometry

• Closest pair problem: find the pair of points (from a set of points) with the smallest distance between them
• Collision detection algorithms: check for the collision or intersection of two given solids
• Cone algorithm: identify surface points
• Convex hull algorithms: determining the convex hull of a set of points
  • Chan's algorithm
  • Gift wrapping algorithm or Jarvis march
  • Graham scan
  • Kirkpatrick–Seidel algorithm
• Euclidean Distance Transform - Computes the distance between every point in a grid and a discrete collection of points.
• Geometric hashing: a method for efficiently finding two-dimensional objects represented by discrete points that have undergone an affine transformation
• Gilbert-Johnson-Keerthi distance algorithm: determining the smallest distance between two convex shapes.
• Jump-and-Walk algorithm: an algorithm for point location in triangulations
• Laplacian smoothing: an algorithm to smooth a polygonal mesh
• Line segment intersection: finding whether lines intersect, usually with a sweep line algorithm
  • Bentley-Ottmann algorithm
  • Shamos-Hoey algorithm
• Minimum bounding box algorithms: find the oriented minimum bounding box enclosing a set of points
• Nearest neighbor search: find the nearest point or points to a query point
• Point in polygon algorithms: tests whether a given point lies within a given polygon
• Rotating calipers: determine all antipodal pairs of points and vertices on a convex polygon or convex hull.
• Triangulation
  • Delaunay triangulation
    • Ruppert's algorithm (also known as Delaunay refinement): create quality Delaunay triangulations
  • Marching triangles: reconstruct two-dimensional surface geometry from an unstructured point cloud
  • Polygon triangulation algorithms: decompose a polygon into a set of triangles
  • Voronoi diagrams, geometric dual of Delaunay triangulation
    • Bowyer-Watson algorithm: create voronoi diagram in any number of dimensions
    • Fortune's Algorithm: create voronoi diagram

[edit] Computer algebra

• Buchberger's algorithm: finds a Gröbner basis
• Cantor–Zassenhaus algorithm: factor polynomials over finite fields
• Faugère_F4_algorithm: finds a Gröbner basis (also mentions the F5 algorithm)
• Gosper's algorithm: find sums of hypergeometric terms that are themselves hypergeometric terms
• Knuth-Bendix completion algorithm: for rewriting rule systems
• Multivariate division algorithm: for polynomials in several indeterminates
• Pollard's lambda algorithm (also known as Pollard's kangaroo algorithm): an algorithm for solving the discrete logarithm problem
• Polynomial long division: an algorithm for dividing a polynomial by another polynomial of the same or lower degree
• Risch algorithm: an algorithm for the calculus operation of indefinite integration (i.e. finding antiderivatives)

[edit] Computer graphics

• Clipping
  • Line clipping
    • Cohen-Sutherland
    • Liang-Barsky
    • Fast-Clipping
    • Cyrus-Beck
    • Nicholl-Lee-Nicholl
  • Polygon Clipping
    • Sutherland-Hodgman
    • Weiler-Atherton
• Contour lines and Isosurfaces
  • Marching cubes: extract a polygonal mesh of an isosurface from a three-dimensional scalar field (sometimes called voxels)
  • Marching squares: generate contour lines for a two-dimensional scalar field
  • Marching tetrahedrons: an alternative to Marching cubes
• Flood fill: fills a connected region of a multi-dimensional array with a specified symbol
• Global illumination algorithms: Considers direct illumination and reflection from other objects.
  • Radiosity
  • Ray tracing
  • Beam tracing
  • Cone tracing
  • Path tracing
  • Metropolis light transport
  • Ambient occlusion
  • Photon mapping
  • Image based lighting
• Hidden surface removal or Visual surface determination
  • Painter's algorithm: detects visible parts of a 3-dimensional scenery
  • Newell's algorithm: eliminate polygon cycles in the depth sorting required in hidden surface removal
  • Scanline rendering: constructs an image by moving an imaginary line over the image
  • Warnock algorithm
• Line Drawing: graphical algorithm for approximating a line segment on discrete graphical media.
  • Bresenham's line algorithm: plots points of a 2-dimensional array to form a straight line between 2 specified points (uses decision variables)
  • DDA line algorithm: plots points of a 2-dimensional array to form a straight line between 2 specified points (uses floating-point math)
  • Xiaolin Wu's line algorithm: algorithm for line antialiasing.
• Midpoint circle algorithm: an algorithm used to determine the points needed for drawing a circle
• Ramer-Douglas-Peucker algorithm: Given a 'curve' composed of line segments to find a curve not too dissimilar but that has fewer points
• Shading
  • Gouraud shading: an algorithm to simulate the differing effects of light and colour across the surface of an object in 3D computer graphics
  • Phong shading: an illumination model and an interpolation method in 3D computer graphics
• Slerp (spherical linear interpolation): quaternion interpolation for the purpose of animating 3D rotation
• Summed Area Table (also known as an Integral Image): is an algorithm for computing sum of values in a rectangular subset of a grid in constant time

[edit] Computer vision

• Connected component labeling: find and label disjoint regions
• Pulse-Coupled Neural Networks (PCNN): neural models proposed by modeling a cat's visual cortex and developed for high-performance biomimetic image processing.
• SIFT (Scale-invariant feature transform): is an algorithm to detect and describe local features in images.

[edit] Cryptographic algorithms

• Asymmetric (public key) encryption:
  • DSA
  • ElGamal
  • NTRUEncrypt
  • RSA
• Cryptographic Message digest functions (hashing functions):
  • HMAC: keyed-hash message authentication
  • MD5 – Note that there is now a method of generating collisions for MD5
  • RIPEMD-160
  • SHA-1
  • Tiger (TTH), usually used in Tiger tree hashes
• Cryptographically secure pseudo-random number generators
  • Blum Blum Shub - based on the hardness of factorization
  • Fortuna, intended as an improvement on Yarrow algorithm
  • Linear feedback shift register
  • Yarrow algorithm
• Key exchange
  • Diffie-Hellman key exchange
• Secret sharing, Secret Splitting, Key Splitting, M of N algorithms
  • Blakey's Scheme
  • Shamir's Scheme
• Symmetric (secret key) encryption:
  • Advanced Encryption Standard (AES), winner of NIST competition, also known as Rijndael
  • Blowfish
  • Data Encryption Standard (DES), sometimes DE Algorithm, winner of NBS selection competition, replaced by AES for most purposes
  • IDEA
  • RC4 (cipher)
  • Tiny Encryption Algorithm

[edit] Digital signal processing

• Adaptive-additive algorithm (AA algorithm): find the spatial frequency phase of an observed wave source
• Discrete Fourier transform: determines the frequencies contained in a (segment of a) signal
  • Bluestein's FFT algorithm
  • Bruun's FFT algorithm
  • Cooley-Tukey FFT algorithm
  • Fast Fourier transform
  • Prime-factor FFT algorithm
  • Rader's FFT algorithm
• Gerchberg–Saxton algorithm: Phase retrieval algorithm for optical planes
• Goertzel algorithm: identify a particular frequency component in a signal. Can be used for DTMF digit decoding.
• Karplus-Strong string synthesis: physical modelling synthesis to simulate the sound of a hammered or plucked string or some types of percussion

[edit] Image Processing

• Dithering and half-toning
  • Error diffusion
  • Floyd-Steinberg dithering
  • Ordered dithering
  • Riemersma dithering
• Elser Difference-Map Algorithm: a search algorithm for general constraint satisfaction problems. Originally used for X-Ray diffraction microscopy
• Feature extraction
  • Canny edge detector: detect a wide range of edges in images
  • Generalised Hough Transform
  • Hough transform
  • Marr-Hildreth algorithm: an early edge detection algorithm
• GrowCut algorithm: an interactive segmentation algorithm
• Osem: algorithm for processing of medical images
• Richardson-Lucy deconvolution: image de-blurring algorithm

[edit] Electronics and hardware algorithms

• Boolean minimization
  • Quine-McCluskey algorithm: Also called as Q-M algorithm, programmable method for simplyfying the boolean equations.
  • Petrick's method: Another algorithm for boolean simplification.
  • Espresso heuristic logic minimization: Fast algorithm for boolean function minimization.
• Computer Architecture
  • Tomasulo algorithm: allows sequential instructions that would normally be stalled due to certain dependencies to execute non-sequentially

[edit] Machine Learning and Statistical Classification

• ALOPEX: a correlation based machine learning algorithm
• Association rule learning: discover interesting relations between variables, used in Data mining
  • Apriori algorithm
  • Eclat algorithm
  • FP-Growth algorithm
  • One-attribute-rule
  • Zero-attribute-rule
• Boosting: Use many weak learners to boost effectiveness
  • AdaBoost: adaptive boosting
  • BrownBoost:a boosting algorithm that may be robust to noisy datasets
  • LogitBoost: logistic regression boosting
  • LPBoost: linear programming boosting
• Bootstrap aggregating (bagging): technique to improve stability and classification accuracy
• Decision Trees
  • C4.5 algorithm: an extension to ID3
  • ID3 algorithm (Iterative Dichotomiser 3): Use heuristic to generate small decision trees
• k-nearest neighbors (k-NN): a method for classifying objects based on closest training examples in the feature space
• Linde-Buzo-Gray algorithm: a vector quantization algorithm used to derive a good codebook
• Locality Sensitive Hashing (LSH): a method of performing probabilistic dimension reduction of high-dimensional data.
• Neural Network
  • Backpropagation: A supervised learning method which requires a teacher that knows, or can calculate, the desired output for any given input
  • Hopfield net: a Recurrent neural network in which all connections are symmetric
  • Perceptron: the simplest kind of feedforward neural network: a linear classifier.
  • Radial basis function network: an artificial neural network that uses radial basis functions as activation functions
  • Self-organizing map: an unsupervised network that produces a low-dimensional representation of the input space of the training samples
• Random forest: classify using many decision trees
• Random multinomial logit: classify using repeated multinomial logit analyses
• Reinforcement Learning:
  • Q-learning: learn an action-value function that gives the expected utility of taking a given action in a given state and following a fixed policy thereafter
  • SARSA (State-Action-Reward-State-Action): learn a Markov decision process policy
  • Temporal difference learning
• Relevance Vector Machine (RVM): similar to SVM, but provides probabilistic classification
• Support Vector Machines (SVM): a set of methods which divide multidimensional data by finding a dividing hyperplane with the maximum margin between the two sets
  • Structured SVM: allows training of a classifier for general structured output labels.

[edit] Number theoretic algorithms

• Binary gcd algorithm: Efficient way of calculating gcd.
• Booth's multiplication algorithm
• Chakravala method: a cyclic algorithm to solve indeterminate quadratic equations, including Pell's equation
• Discrete logarithm:
  • Baby-step giant-step
  • Index calculus algorithm
  • Pollard's rho algorithm for logarithms
  • Pohlig-Hellman algorithm
• Euclidean algorithm: computes the greatest common divisor
• Extended Euclidean algorithm: Also solves the equation ax+by = c.
• Integer factorization: breaking an integer into its prime factors
  • Congruence of squares
  • Dixon's algorithm
  • Fermat's factorization method
  • General number field sieve
  • Lenstra elliptic curve factorization
  • Pollard's p − 1 algorithm
  • Pollard's rho algorithm
  • prime factorization algorithm
  • Quadratic sieve
  • Special number field sieve
  • Trial division
• Multiplication algorithms: fast multiplication of two numbers
• Odlyzko-Schönhage algorithm: calculates nontrivial zeroes of the Riemann zeta function
• Primality tests: determining whether a given number is prime
  • AKS primality test
  • Miller-Rabin primality test
  • Sieve of Atkin
  • Sieve of Eratosthenes

[edit] Numerical algorithms

[edit] Elementary and Special Functions

• Computation of π:
  • Borwein's algorithm: an algorithm to calculate the value of 1/π
  • Gauss–Legendre algorithm: computes the digits of pi
  • Bailey–Borwein–Plouffe formula: (BBP formula) a spigot algorithm for the computation of the nth binary digit of π
• Hyperbolic and Trigonometric Functions:
  • BKM algorithm: compute elementary functions using a table of logarithms
  • CORDIC: compute hyperbolic and trigonometric functions using a table of arctangents
• Exponentiation:
  • Addition-chain exponentiation exponentiation by positive integer powers that requires a minimal number of multiplications
  • Exponentiating by squaring: an algorithm used for the fast computation of large integer powers of a number
• Montgomery reduction: an algorithm that allows modular arithmetic to be performed efficiently when the modulus is large
• Multiplication algorithms: fast multiplication of two numbers
  • Booth's multiplication algorithm: a multiplication algorithm that multiplies two signed binary numbers in two's complement notation
  • Fürer's algorithm: an integer multiplication algorithm for very large numbers possessing a very low asymptotic complexity
  • Karatsuba algorithm: an efficient procedure for multiplying large numbers
  • Schönhage-Strassen algorithm: an asymptotically fast multiplication algorithm for large integers
  • Toom–Cook multiplication: (Toom3) a multiplication algorithm for large integers
• Rounding functions: the classic ways to round numbers
• Spigot algorithm: A way to compute the value of a mathematical constant without knowing preceding digits
• Square and Nth root of a number:
  • Alpha max plus beta min algorithm: an approximation of the square-root of the sum of two squares
  • Methods of computing square roots
  • nth root algorithm
  • Shifting nth-root algorithm: digit by digit root extraction

• Summation:
  • Binary splitting: a divide and conquer technique which speeds up the numerical evaluation of many types of series with rational terms
  • Kahan summation algorithm: a more accurate method of summing floating-point numbers

[edit] Geometric

• Level set method (LSM): a numerical technique for tracking interfaces and shapes

[edit] Interpolation and Extrapolation

• Birkhoff interpolation: an extension of polynomial interpolation
• Cubic interpolation
• Hermite interpolation
• Linear interpolation: a method of curve fitting using linear polynomials
• Monotone cubic interpolation: a variant of cubic interpolation that preserves monotonicity of the data set being interpolated.
• Multivariate interpolation
  • Bicubic interpolation, a generalization of cubic interpolation to two dimensions
  • Bilinear interpolation: an extension of linear interpolation for interpolating functions of two variables on a regular grid
  • Lanczos resampling ("Lanzosh"): a multivariate interpolation method used to compute new values for any digitally sampled data
  • Nearest-neighbor interpolation
  • Tricubic interpolation, a generalization of cubic interpolation to three dimensions
• Pareto interpolation: a method of estimating the median and other properties of a population that follows a Pareto distribution.
• Polynomial interpolation
  • Neville's algorithm
• Spline interpolation: Reduces error with Runge's phenomenon.
  • De Boor algorithm: B-splines
  • De Casteljau's algorithm: Bézier splines
• Trigonometric interpolation

[edit] Numerical Integration

• MISER algorithm: Monte Carlo simulation, numerical integration
• Multigrid methods: (MG methods): a group of algorithms for solving differential equations using a hierarchy of discretizations
• Verlet integration (IPA: [veʁ'le]): integrate Newton's equations of motion

[edit] Linear Algebra

• Biconjugate gradient method: solves systems of linear equations
• Coppersmith–Winograd algorithm: square matrix multiplication
• Eigenvalue algorithms
  • Arnoldi iteration
  • Inverse iteration
  • Jacobi method
  • Lanczos iteration
  • QR algorithm
  • Rayleigh quotient iteration
• Solving systems of linear equations
  • Conjugate gradient: an algorithm for the numerical solution of particular systems of linear equations
  • Gaussian elimination
  • Gauss–Jordan elimination: solves systems of linear equations
  • Gauss–Seidel method: solves systems of linear equations iteratively
  • Levinson recursion: solves equation involving a Toeplitz matrix
  • Stone's method: also known as the strongly implicit procedure or SIP, is an algorithm for solving a sparse linear system of equations
  • Successive over-relaxation (SOR): method used to speed up convergence of the Gauss–Seidel method
  • Tridiagonal matrix algorithm (Thomas algorithm): solves systems of tridiagonal equations
• Gram-Schmidt process: orthogonalizes a set of vectors
• Strassen algorithm: faster matrix multiplication
• Symbolic Cholesky decomposition: Efficient way of storing sparse matrix

[edit] Monte Carlo

• Gibbs sampling: generate a sequence of samples from the joint probability distribution of two or more random variables
• Metropolis–Hastings algorithm: used to generate a sequence of samples from the probability distribution of one or more variables

[edit] Root Finding

• False position method: approximates roots of a function
• Newton's method: finds zeros of functions with calculus
• Secant method: approximates roots of a function

[edit] Optimization algorithms

• Alpha-beta pruning: search to reduce number of nodes in minimax algorithm
• Branch and bound
• Chain matrix multiplication
• Combinatorial optimization: optimization problems where the set of feasible solutions is discrete
  • Greedy randomized adaptive search procedure (GRASP): successive constructions of a greedy randomized solution and subsequent iterative improvements of it through a local search
  • Hungarian method: a combinatorial optimization algorithm which solves the assignment problem in polynomial time
• Constraint satisfaction
  • General algorithms for the constraint satisfaction
    • AC-3 algorithm
    • Difference map algorithm
    • Min conflicts algorithm
  • Chaff algorithm: an algorithm for solving instances of the boolean satisfiability problem
  • Davis–Putnam algorithm: check the validity of a first-order logic formula
  • Davis-Putnam-Logemann-Loveland algorithm (DPLL): an algorithm for deciding the satisfiability of propositional logic formulae in conjunctive normal form, i.e. for solving the CNF-SAT problem
• Cross-entropy method: a general Monte Carlo approach to combinatorial and continuous multi-extremal optimization and importance sampling
• Dancing Links: finds all solutions to the exact cover problem
• Differential evolution
• Dynamic Programming: problems exhibiting the properties of overlapping subproblems and optimal substructure
• Ellipsoid method: is an algorithm for solving convex optimization problems
• Evolutionary computation: optimization inspired by biological mechanisms of evolution
  • Evolution strategy
  • Genetic algorithms
    • Fitness proportionate selection - also known as roulette-wheel selection
    • Stochastic universal sampling
    • Truncation selection
    • Tournament selection
  • Swarm intelligence
    • Ant colony optimization
    • Bees algorithm: a search algorithm which mimics the food foraging behaviour of swarms of honey bees
    • Particle swarm
• Gradient descent
• Harmony search (HS): a metaheuristic algorithm mimicking the improvisation process of musicians
• Interior point method
• Linear programming
  • Dantzig-Wolfe decomposition: an algorithm for solving linear programming problems with special structure
  • Delayed column generation
  • Integer linear programming: solve linear programming problems where some or all the unknowns are restricted to integer values
    • Branch and cut
    • Cutting-plane method
  • Karmarkar's algorithm: The first reasonably efficient algorithm that solves the linear programming problem in polynomial time.
  • Simplex algorithm: An algorithm for solving the linear programming problem
• Line search
• Local search: a metaheuristic for solving computationally hard optimization problems
  • Random-restart hill climbing
  • Tabu search
• Minimax used in game programming
• Nearest neighbor search (NNS): find closest points in a metric space
• Newton's method in optimization
• Nonlinear optimization
  • BFGS method: A nonlinear optimization algorithm
  • Gauss–Newton algorithm: An algorithm for solving nonlinear least squares problems.
  • Levenberg–Marquardt algorithm: An algorithm for solving nonlinear least squares problems.
  • Nelder-Mead method (downhill simplex method): A nonlinear optimization algorithm
• Odds algorithm (Bruss algorithm) : Finds the optimal strategy to predict a last specific event in a random sequence event
• Simulated annealing
• Stochastic tunneling
• Subset sum algorithm

[edit] Programming Language Theory

• C3 linearization: an algorithm used primarily to obtain a consistent linearization of a multiple inheritance hierarchy in object-oriented programming
• Chaitin's algorithm: a bottom-up, graph coloring register allocation algorithm that uses cost/degree as its spill metric
• Hindley–Milner type inference algorithm
• Rete algorithm: an efficient pattern matching algorithm for implementing production rule systems
• Sethi-Ullman algorithm: generate optimal code for arithmetic expressions

[edit] Parsing

• CYK algorithm: An O(n³) algorithm for parsing context-free grammars in Chomsky normal form
• Earley parser: Another O(n³) algorithm for parsing any context-free grammar
• GLR parser:An algorithm for parsing any context-free grammar by Masaru Tomita. It is tuned for deterministic grammars, on which it performs almost linear time and O(n³) in worst case.
• Inside-outside algorithm: An O(n³) algorithm for re-estimating production probabilities in probabilistic context-free grammars
• LL parser: A relatively simple linear time parsing algorithm for a limited class of context-free grammars
• LR parser: A more complex linear time parsing algorithm for a larger class of context-free grammars. Variants:
  • Canonical LR parser
  • LALR (Look-ahead LR) parser
  • Operator-precedence parser
  • SLR (Simple LR) parser
• Packrat parser: A linear time parsing algorithm supporting some context-free grammars and parsing expression grammars
• Recursive descent parser: A top-down parser suitable for LL(k) grammars
• Shunting yard algorithm: convert an infix-notation math expression to postfix

[edit] Quantum algorithms

Application of quantum computation to various categories of problems and algorithms

• Deutsch-Jozsa algorithm: criterion of balance for Boolean function
• Grover's algorithm: provides quadratic speedup for many search problems
• Shor's algorithm: provides exponential speedup (relative to currently known non-quantum algorithms) for factoring a number

[edit] Science and Medicine

[edit] Astronomy

• Doomsday algorithm: day of the week
• Zeller's congruence is an algorithm to calculate the day of the week for any Julian or Gregorian calendar date

[edit] Geoscience

• Vincenty's formulae: a fast algorithm to calculate the distance between two latitude/longitude points on an ellipsoid

[edit] Physics

• Rainflow-counting algorithm: Reduces a complex stress history to a count of elementary stress-reversals for use in fatigue analysis
• Fast multipole method (FMM): speed up the calculation of long-ranged forces in the n-body problem

[edit] Linguistics

• Lesk algorithm: word sense disambiguation
• Stemming algorithm: a method of reducing words to their stem, base, or root form

[edit] Medicine

• Texas Medication Algorithm Project

[edit] Software engineering

• Unicode Collation Algorithm
• CHS conversion: converting between disk addressing systems
• Double dabble: Convert binary numbers to BCD
• Hash Function: convert a large, possibly variable-sized amount of data into a small datum, usually a single integer that may serve as an index into an array
  • Fowler Noll Vo hash: fast with low collision rate
  • Pearson hashing: computes 8 bit value only, optimized for 8 bit computers
  • Zobrist hashing: used in the implementation of transposition tables
• Cache algorithms
• Xor swap algorithm: swaps the values of two variables without using a buffer

[edit] Database algorithms

• Algorithms for Recovery and Isolation Exploiting Semantics (ARIES): transaction recovery
• Join algorithms
  • Block nested loop
  • Hash join
  • Nested loop join
  • Sort-Merge Join

[edit] Distributed systems algorithms

• Bully algorithm: a method for dynamically selecting a coordinator
• Byzantine fault tolerance: good fault tolerance.
• Clock synchronization
  • Berkeley algorithm
  • Cristian's algorithm
  • Intersection algorithm
  • Marzullo's algorithm
• Lamport ordering: a partial ordering of events based on the happened-before relation
• Mutual exclusion
  • Lamport's Distributed Mutual Exclusion Algorithm
  • Maekawa's Algorithm
  • Raymond's Algorithm
  • Ricart-Agrawala Algorithm
• Paxos algorithm: a family of protocols for solving consensus in a network of unreliable processors
• Snapshot algorithm: record a consistent global state for an asynchronous system
• Detection of Process Termination
  • Dijkstra-Scholten algorithm
  • Huang's algorithm
• Vector clocks: generate a partial ordering of events in a distributed system and detect causality violations

[edit] Memory Allocation and deallocation algorithms

• Buddy memory allocation: Algorithm to allocate memory such that fragmentation is less.
• Garbage collectors
  • Boehm garbage collector: Conservative garbage collector
  • Cheney's algorithm: An improvement on the Semi-space collector
  • Generational garbage collector: Fast garbage collectors that segregate memory by age
  • Mark-compact algorithm: a combination of the mark-sweep algorithm and Cheney's copying algorithm
  • Mark and sweep
  • Semi-space collector: An early copying collector
• Reference counting

[edit] Operating systems algorithms

• Banker's algorithm: Algorithm used for deadlock avoidance.
• Bully algorithm: Selecting new leader among many computers.
• Page replacement algorithms: Selecting the victim page under low memory conditions.
  • Adaptive Replacement Cache: better performance than LRU

[edit] Disk scheduling algorithms:

• Elevator algorithm: Disk scheduling algorithm that works like an elevator.
• Shortest seek first: Disk scheduling algorithm to reduce seek time.

[edit] Networking algorithms

• Karn's Algorithm: addresses the problem of getting accurate estimates of the round-trip time for messages when using TCP
• Luleå algorithm: a technique for storing and searching internet routing tables efficiently
• Network congestion
  • Exponential backoff
  • Nagle's algorithm: improve the efficiency of TCP/IP networks by coalescing packets
  • Truncated binary exponential backoff
• Traffic shaping and Rate limiting
  • Leaky bucket
  • Token bucket

[edit] Process synchronization algorithms:

• Dekker's algorithm
• Lamport's Bakery algorithm
• Peterson's algorithm

[edit] Scheduling algorithms

• Earliest deadline first scheduling
• Fair-share scheduling
• Least slack time scheduling
• List scheduling
• Multi level feedback queue
• Rate-monotonic scheduling
• Rayrole's algorithm: resource calendar management
• Round-robin scheduling
• shortest job next
• shortest remaining time

[edit] Statistical Algorithms

• Algorithms for calculating variance: avoiding instability and numerical overflow
• Approximate counting algorithm: Allows counting large number of events in a small register
• Clustering Algorithms
  • Canopy clustering algorithm: an unsupervised clustering algorithm related to the K-means algorithm
  • Fuzzy clustering: a class of clustering algorithms where each point has a degree of belonging to clusters
    • Fuzzy c-means
    • FLAME clustering (Fuzzy clustering by Local Approximation of MEmberships): define clusters in the dense parts of a dataset and perform cluster assignment solely based on the neighborhood relationships among objects
  • k-means algorithm: cluster objects based on attributes into partitions
  • k-medoids: similar to k-means, but chooses datapoints or medoids as centers
  • Linde-Buzo-Gray algorithm: a vector quantization algorithm to derive a good codebook
  • Lloyd's algorithm (Voronoi iteration or relaxation): group data points into a given number of categories.
  • Single-linkage clustering: a simple agglomerative clustering algorithm
  • QT clustering: partitions without the number of clusters a priori
• Estimation Theory
  • Expectation-maximization algorithm A class of related algorithms for finding maximum likelihood estimates of parameters in probabilistic models
    • Ordered subset expectation maximization (OSEM): used in medical imaging for positron emission tomography, single photon emission computed tomography and X-ray computed tomography.
  • Odds algorithm (Bruss algorithm) Optimal online search for distinguished value in sequential random input
  • Kalman filter: estimate the state of a dynamic system from a series of noisy measurements
• False nearest neighbor algorithm (FNN) estimates fractal dimension
• Hidden Markov Model
  • Baum-Welch algorithm: compute maximum likelihood estimates and posterior mode estimates for the parameters of a hidden markov model
  • Forward-backward algorithm a dynamic programming algorithm for computing the probability of a particular observation sequence
  • Viterbi algorithm: find the most likely sequence of hidden states in a hidden markov model

[edit] Theory of computation and automata

• Powerset construction: Algorithm to convert nondeterministic automaton to deterministic automaton.
• Tarski–Kuratowski algorithm: a non-deterministic algorithm which provides an upper bound for the complexity of formulas in the arithmetical hierarchy and analytical hierarchy

[edit] Other

• Rutishauser's algorithm

[edit] See also

• Algorithm
• Heuristic