List of algorithms

The following is a list of algorithms along with one-line descriptions for each.

Combinatorial algorithms

Further information: Combinatorics

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: solves the stable marriage problem
• Pseudorandom number generators (uniformly distributed):
  • Blum Blum Shub
  • Lagged Fibonacci generator
  • Linear congruential generator
  • Mersenne twister

Graph algorithms

Further information: Graph theory and Category: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
• Prüfer coding: conversion between a labeled tree and its Prüfer sequence
• 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.

Graph drawing

Further information: Graph drawing

• Force-based algorithms (also known as force-directed algorithms or spring-based algorithm)
• Spectral layout

Network theory

Further information: 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
  • Dinic's algorithm: is a strongly polynomial algorithm for computing the maximum flow in a flow network.
  • 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
  • Push–relabel algorithm: computes a maximum flow in a graph

Routing for Graphs

• Edmonds's algorithm (also known as Chu–Liu/Edmonds's algorithm): find maximum or minimum branchings
• Euclidean minimum spanning tree: algorithms for computing the minimum spanning tree of a set of points in the plane
• Longest path problem: find a simple path of maximum length in a given graph
• Minimum spanning tree
  • Boruvka's algorithm
  • Kruskal's algorithm
  • Prim's algorithm
  • Reverse-delete 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
• Transitive closure problem: find the transitive closure of a given binary relation
• Traveling salesman problem
  • Christofides algorithm
  • Nearest neighbour algorithm
• Warnsdorff's algorithm: A heuristic method for solving the Knight's Tour problem.

Graph Search

Further information: State space search and Graph search algorithm

• A*: special case of best-first search that uses heuristics to improve speed
• B*: 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
• Beam search: is a heuristic search algorithm that is an optimization of best-first search that reduces its memory requirement
• Beam stack search: integrates backtracking with beam search
• Best-first search: traverses a graph in the order of likely importance using a priority queue
• Bidirectional search: find the shortest path from an initial vertex to a goal vertex in a directed graph
• Bloom filter: a constant time and memory check to see whether a given element exists in a set. May return a false positive, but never a false negative.
• Breadth-first search: traverses a graph level by level
• D*: an incremental heuristic search algorithm
• Depth-first search: traverses a graph branch by branch
• Dijkstra's algorithm: A special case of A* for which no heuristic function is used
• General Problem Solver: a seminal theorem-proving algorithm intended to work as a universal problem solver machine.
• Iterative deepening depth-first search (IDDFS): a state space search strategy
• Lexicographic breadth-first search (also known as Lex-BFS): a linear time algorithm for ordering the vertices of a graph
• Uniform-cost search: a tree search that finds the lowest cost route where costs vary
• SSS*: state space search traversing a game tree in a best-first fashion similar to that of the A* search algorithm

Subgraphs

• Bron–Kerbosch algorithm: a technique for finding maximal cliques in an undirected graph
• Strongly connected components
  • Path-based strong component algorithm
  • Kosaraju's algorithm
  • Tarjan's strongly connected components algorithm

Sequence algorithms

Further information: Sequences

Approximate sequence matching

• Bitap algorithm: fuzzy algorithm that determines if strings are approximately equal.
• Phonetic algorithms
  • Daitch–Mokotoff Soundex: a Soundex refinement which allows matching of Slavic and Germanic surnames
  • Double Metaphone: an improvement on Metaphone
  • Match Rating Approach: a phonetic algorithm developed by Western Airlines
  • 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
• 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
• Trigram search: search for text when the exact syntax or spelling of the target object is not precisely known

Sequence search

• Linear search: finds an item in an unsorted sequence
• Selection algorithm: finds the kth largest item in a sequence
• Ternary search: a technique for finding the minimum or maximum of a function that is either strictly increasing and then strictly decreasing or vice versa
• Sorted lists
  • Binary search algorithm: locates an item in a sorted sequence
  • Fibonacci search technique: search a sorted sequence using a divide and conquer algorithm that narrows down possible locations with the aid of Fibonacci numbers
  • Jump search (or block search): linear search on a smaller subset of the sequence
  • 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.
  • Uniform binary search: an optimization of the classic binary search algorithm

Sequence Merging

Main article: Merge algorithm

• Simple Merge algorithm
• k-way Merge algorithm
• Union (merge, with elements on the output not repeated)

Sequence Permutations

Further information: Permutations

• Fisher–Yates shuffle (also known as the Knuth shuffle): randomly shuffle a finite set
• Schensted algorithm: constructs a pair of Young tableaux from a permutation
• Steinhaus–Johnson–Trotter algorithm (also known as the Johnson–Trotter algorithm): generate permutations by transposing elements

Sequence alignment

• Dynamic time warping: measure similarity between two sequences which may vary in time or speed
• 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

Sequence Sorting

Main article: 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
  • Timsort: adaptative algorithm derived from merge sort and insertion sort. Used in Python 2.3 and up, and Java SE 7.
• 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
  • Cycle sort: in-place with theoretically optimal number of writes
• 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
• Unknown class
  • Samplesort

Subsequences

Further information: Subsequence

• 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 increasing subsequence problem: find the longest increasing subsequence of a given sequence
• Shortest common supersequence problem: Find the shortest supersequence that contains two or more sequences as subsequences

Substrings

Further information: Substring

• Longest common substring problem: find the longest string (or strings) that is a substring (or are substrings) of two or more strings
• Substring search
  • Aho–Corasick string matching algorithm: trie based algorithm for finding all substring matches to any of a finite set of strings
  • Boyer–Moore string search algorithm: amortized 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 string matching algorithm: a variant of the Boyer–Moore
• Ukkonen's algorithm: a linear-time, online algorithm for constructing suffix trees

Computational mathematics

Further information: Computational mathematics

See also: Combinatorial algorithms and Computational science

Abstract algebra

Further information: 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.

Computer algebra

Further information: 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 kangaroo algorithm (also known as Pollard's lambda 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)

Geometry

Main page: Geometric algorithms

Further information: 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
  • Graham scan
  • QuickHull
  • Gift wrapping algorithm or Jarvis march
  • Chan's algorithm
  • 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.
• Shoelace algorithm: determine the area of a polygon whose vertices are described by ordered pairs in the plane
• Triangulation
  • Delaunay triangulation
    • Ruppert's algorithm (also known as Delaunay refinement): create quality Delaunay triangulations
    • Chew's second algorithm: create quality constrained 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
  • Quasitriangulation

Number theoretic algorithms

Further information: Number theory

• 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
  • Shor's algorithm
  • Special number field sieve
  • Trial division
• Multiplication algorithms: fast multiplication of two numbers
  • Karatsuba algorithm
  • Schönhage–Strassen algorithm
  • Toom–Cook multiplication
• Odlyzko–Schönhage algorithm: calculates nontrivial zeroes of the Riemann zeta function
• Primality tests: determining whether a given number is prime
  • AKS primality test
  • Baillie-PSW primality test
  • Fermat primality test
  • Lucas primality test
  • Miller–Rabin primality test
  • Sieve of Atkin
  • Sieve of Eratosthenes
  • Sieve of Sundaram

Numerical algorithms

Further information: Numerical analysis and List of numerical analysis topics

Differential equation solving

Further information: Differential equation

• Euler method
• Backward Euler method
• Trapezoidal rule (differential_equations)

• Linear multistep methods
• Runge–Kutta methods
  • Euler integration
• Multigrid methods (MG methods), a group of algorithms for solving differential equations using a hierarchy of discretizations
• Partial differential equation:
  • Finite difference method
  • Crank-Nicolson method for diffusion equations
  • Lax-Wendroff for wave equations
• Verlet integration (French pronunciation: ​[vɛʁˈlɛ]): integrate Newton's equations of motion

Elementary and special functions

Further information: 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

Geometric

• Filtered back-projection: efficiently compute the inverse 2-dimensional Radon transform.
• Level set method (LSM): a numerical technique for tracking interfaces and shapes

Interpolation and extrapolation

Further information: 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

Linear algebra

Further information: Numerical linear algebra

• Eigenvalue algorithms
  • Arnoldi iteration
  • Inverse iteration
  • Jacobi method
  • Lanczos iteration
  • Power iteration
  • QR algorithm
  • Rayleigh quotient iteration
• Gram–Schmidt process: orthogonalizes a set of vectors
• Matrix multiplication
  • Cannon's algorithm: a distributed algorithm for matrix multiplication especially suitable for computers laid out in an N × N mesh
  • Coppersmith–Winograd algorithm: square matrix multiplication
  • Freivalds' algorithm: a randomized algorithm used to verify matrix multiplication
  • Strassen algorithm: faster matrix multiplication
• Solving systems of linear equations
  • Biconjugate gradient method: solves 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
• Sparse matrix algorithms
  • Cuthill–McKee algorithm: reduce the bandwidth of sparse symmetric matrices
  • Minimum degree algorithm: permute the rows and columns of a symmetric sparse matrix before applying the Cholesky decomposition
  • Symbolic Cholesky decomposition: Efficient way of storing sparse matrix

Monte Carlo

Further information: Monte Carlo method

• 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
• Wang and Landau algorithm: an extension of Metropolis–Hastings algorithm sampling

Numerical integration

Further information: Numerical integration

• MISER algorithm: Monte Carlo simulation, numerical integration

Root finding

Main article: Root-finding algorithm

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

Optimization algorithms

Main article: Mathematical optimization

• Alpha-beta pruning: search to reduce number of nodes in minimax algorithm
• Branch and bound
• Bruss algorithm: see odds algorithm
• 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 formula in conjunctive normal form, i.e. for solving the CNF-SAT problem
  • Exact cover problem
    • Algorithm X: a nondeterministic algorithm
    • Dancing Links: an efficient implementation of Algorithm X
• Cross-entropy method: a general Monte Carlo approach to combinatorial and continuous multi-extremal optimization and importance sampling
• 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
  • Gene expression programming
  • Genetic algorithms
    • Fitness proportionate selection - also known as roulette-wheel selection
    • Stochastic universal sampling
    • Truncation selection
    • Tournament selection
  • Memetic algorithm
  • Swarm intelligence
    • Ant colony optimization
    • Bees algorithm: a search algorithm which mimics the food foraging behavior 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
  • Benson's algorithm: an algorithm for solving linear vector optimization problems
  • 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 linear programming problems
• 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
  • Best Bin First: find an approximate solution to the Nearest neighbor search problem in very high dimensional spaces
• 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

Computational science

Further information: Computational science

Astronomy

Main article: Astronomical algorithms

• 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
• various Easter algorithms are used to calculate the day of Easter

Bioinformatics

Further information: Bioinformatics

See also: Sequence alignment algorithms

• Basic Local Alignment Search Tool also known as BLAST: an algorithm for comparing primary biological sequence information
• Kabsch algorithm: calculate the optimal alignment of two sets of points in order to compute the root mean squared deviation between two protein structures.
• Velvet: a set of algorithms manipulating de Bruijn graphs for genomic sequence assembly
• Sorting by signed reversals: an algorithm for understanding genomic evolution.

Geoscience

Further information: Geoscience

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

Linguistics

Further information: Computational linguistics and Natural language processing

• Lesk algorithm: word sense disambiguation
• Stemming algorithm: a method of reducing words to their stem, base, or root form
• Sukhotin's algorithm: a statistical classification algorithm for classifying characters in a text as vowels or consonants

Medicine

Further information: Medical algorithms

• ESC algorithm for the diagnosis of heart failure
• Manning Criteria for irritable bowel syndrome
• Pulmonary embolism diagnostic algorithms
• Texas Medication Algorithm Project

Physics

Further information: Computational physics

• Constraint algorithm: a class of algorithms for satisfying constraints for bodies that obey Newton's equations of motion
• Demon algorithm: a Monte Carlo method for efficiently sampling members of a microcanonical ensemble with a given energy
• Featherstone's algorithm: compute the effects of forces applied to a structure of joints and links
• Ground state approximation
  • Variational method
    • Ritz method
• N-body problems
  • Barnes–Hut simulation: Solves the n-body problem in an approximate way that has the order O(n log n) instead of O(n²) as in a direct-sum simulation.
  • Fast multipole method (FMM): speeds up the calculation of long-ranged forces
• Rainflow-counting algorithm: Reduces a complex stress history to a count of elementary stress-reversals for use in fatigue analysis
• Sweep and prune: a broad phase algorithm used during collision detection to limit the number of pairs of solids that need to be checked for collision
• VEGAS algorithm: a method for reducing error in Monte Carlo simulations

Statistics

Further information: Computational statistics

• Algorithms for calculating variance: avoiding instability and numerical overflow
• Approximate counting algorithm: Allows counting large number of events in a small register
• Bayesian statistics
  • Nested sampling algorithm: a computational approach to the problem of comparing models in Bayesian statistics
• Clustering Algorithms
  • Average-linkage clustering: a simple agglomerative clustering algorithm
  • Canopy clustering algorithm: an unsupervised pre-clustering algorithm related to the K-means algorithm
  • Complete-linkage clustering: a simple agglomerative clustering algorithm
  • DBSCAN: a density based clustering algorithm
  • Expectation-maximization 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 clustering: cluster objects based on attributes into partitions
  • k-means++: a variation of this, using modified random seeds
  • 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, a popular algorithm for k-means clustering
  • OPTICS: a density based clustering algorithm with a visual evaluation method
  • Single-linkage clustering: a simple agglomerative clustering algorithm
  • SUBCLU: a subspace clustering algorithm
  • Ward's method : an agglomerative clustering algorithm, extended to more general Lance–Williams algorithms
• 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
• Partial least squares regression: finds a linear model describing some predicted variables in terms of other observable variables
• Queuing theory
  • Buzen's algorithm: an algorithm for calculating the normalization constant G(K) in the Gordon–Newell theorem
• RANSAC (an abbreviation for "RANdom SAmple Consensus"): an iterative method to estimate parameters of a mathematical model from a set of observed data which contains outliers
• Scoring algorithm: is a form of Newton's method used to solve maximum likelihood equations numerically
• Yamartino method: calculate an approximation to the standard deviation σθ of wind direction θ during a single pass through the incoming data
• Ziggurat algorithm: generate random numbers from a non-uniform distribution

Computer science

Further information: Computer science

Computer architecture

Further information: Computer architecture

• Tomasulo algorithm: allows sequential instructions that would normally be stalled due to certain dependencies to execute non-sequentially

Computer graphics

Further information: Computer graphics

• Clipping
  • Line clipping
    • Cohen–Sutherland
    • Cyrus–Beck
    • Fast-clipping
    • Liang–Barsky
    • Nicholl–Lee–Nicholl
  • Polygon clipping
    • Sutherland–Hodgman
    • Vatti
    • 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
• Discrete Green's Theorem: is an algorithm for computing double integral over a generalized rectangular domain in constant time. It is a natural extension to the summed area table algorithm
• 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.
  • Ambient occlusion
  • Beam tracing
  • Cone tracing
  • Image-based lighting
  • Metropolis light transport
  • Path tracing
  • Photon mapping
  • Radiosity
  • Ray tracing
• Hidden surface removal or Visual surface determination
  • Newell's algorithm: eliminate polygon cycles in the depth sorting required in hidden surface removal
  • Painter's algorithm: detects visible parts of a 3-dimensional scenery
  • 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 algorithm to interpolate surface normal-vectors for surface shading 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): an algorithm for computing the sum of values in a rectangular subset of a grid in constant time

Cryptography

Further information: Cryptography and Topics in cryptography

• Asymmetric (public key) encryption:
  • DSA
  • ElGamal
  • Elliptic curve cryptography
  • NTRUEncrypt
  • RSA
• Cryptographic hash functions:
  • HMAC: keyed-hash message authentication
  • MD5 – Note that there is now a method of generating collisions for MD5
  • RIPEMD-160
  • SHA-1
  • SHA-2 (SHA-224, SHA-256, SHA-384, SHA-512)
  • 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

Digital logic

• Boolean minimization
  • Quine–McCluskey algorithm: Also called as Q-M algorithm, programmable method for simplifying the boolean equations.
  • Petrick's method: Another algorithm for boolean simplification.
  • Espresso heuristic logic minimizer: Fast algorithm for boolean function minimization.

Machine learning and statistical classification

Further information: 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 (meta-algorithm): 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.
  • Pulse-coupled neural networks (PCNN): neural models proposed by modeling a cat's visual cortex and developed for high-performance biomimetic image processing.
  • 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.
• Winnow algorithm: related to the perceptron, but uses a multiplicative weight-update scheme

Programming language theory

Further information: 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

Parsing

Further information: 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
  • Simple precedence 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
• Pratt parser
• [[Simpler compiler at Lexical Analysis Tool [i].code =greater code there is -code by Swedes]]

Quantum algorithms

Further information: Quantum algorithm

• 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
• Simon's algorithm: provides a provably exponential speedup (relative to any non-quantum algorithm) for a black-box problem

Theory of computation and automata

Further information: Theory of computation

• 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

Information theory and signal processing

Main articles: Information theory and Signal processing

Coding theory

Further information: Coding theory

Error detection and correction

Further information: Error detection and correction

• 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)
• Forward error correction
• Gray code
• 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
• Redundancy checks
  • Adler-32
  • Cyclic redundancy check
  • Damm algorithm
  • Fletcher's checksum
  • Longitudinal redundancy check (LRC)
  • 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

Lossless compression algorithms

Main page: 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 algorithm: Optimizes Huffman coding subject to a length restriction on code strings
  • Shannon–Fano coding
  • Shannon–Fano–Elias coding: precursor to arithmetic encoding
• 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

Lossy compression algorithms

Main page: 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

Digital signal processing

Further information: 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
• Fast folding algorithm: an efficient algorithm for the detection of approximately periodic events within time series data
• 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

Image processing

Further information: Image processing

• Contrast Enhancement
  • Histogram equalization: use histogram to improve image contrast
  • Adaptive histogram equalization: histogram equalization which adapts to local changes in contrast
• Connected-component labeling: find and label disjoint regions
• 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 detection
  • Canny edge detector: detect a wide range of edges in images
  • Generalised Hough transform
  • Hough transform
  • Marr–Hildreth algorithm: an early edge detection algorithm
  • SIFT (Scale-invariant feature transform): is an algorithm to detect and describe local features in images.
• Richardson–Lucy deconvolution: image de-blurring algorithm
• Seam carving: content-aware image resizing algorithm
• Segmentation: partition a digital image into two or more regions
  • GrowCut algorithm: an interactive segmentation algorithm
  • Random walker algorithm
  • Region growing
  • Watershed transformation: a class of algorithms based on the watershed analogy

Software engineering

Further information: Software engineering

• Cache algorithms
• 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 function: 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
• Unicode Collation Algorithm
• Xor swap algorithm: swaps the values of two variables without using a buffer

Database algorithms

Further information: Database

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

Distributed systems algorithms

Further information: Distributed systems

• 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
• Detection of Process Termination
  • Dijkstra-Scholten algorithm
  • Huang's algorithm
• Lamport ordering: a partial ordering of events based on the happened-before relation
• Mutual exclusion
  • Lamport's Distributed Mutual Exclusion Algorithm
  • Naimi-Trehel's log(n) 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
• Vector clocks: generate a partial ordering of events in a distributed system and detect causality violations

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

Operating systems algorithms

Further information: Operating systems

• Banker's algorithm: Algorithm used for deadlock avoidance.
• Page replacement algorithms: Selecting the victim page under low memory conditions.
  • Adaptive replacement cache: better performance than LRU
  • Clock with Adaptive Replacement (CAR): is a page replacement algorithm that has performance comparable to Adaptive replacement cache

Disk scheduling

Further information: Disk scheduling

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

Networking

Further information: Computer Network

• 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

Process synchronization

Further information: Process synchronization

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

Scheduling

Further information: Scheduling (computing)

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

See also

• List of data structures
• List of machine learning algorithms
• List of algorithm general topics
• List of terms relating to algorithms and data structures
• Heuristic