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Fields

Concepts

Orientations

Models

Developmental	Agile EUP Executable UML Incremental model Iterative model Prototype model RAD UP Scrum Spiral model V-model Waterfall model XP Model-driven engineering Round-trip engineering
Other	SPICE CMMI Data model ER model Function model Information model Metamodeling Object model Systems model View model
Languages	IDEF UML USL SysML

Related fields

v t e Systems engineering
Subfields	Aerospace engineering Biological systems engineering Cognitive systems engineering Configuration management Earth systems engineering and management Electrical engineering Enterprise systems engineering Health systems engineering Performance engineering Reliability engineering Safety engineering Sociocultural Systems Engineering
Processes	Requirements engineering Functional specification System integration Verification and validation Design review System of systems engineering
Concepts	Business process Fault tolerance System System lifecycle V-Model Systems development life cycle
Tools	Decision-making Function modelling IDEF Optimization Quality function deployment System dynamics Systems Modeling Language Systems analysis Systems modeling Work breakdown structure
People	James S. Albus Ruzena Bajcsy Benjamin S. Blanchard Wernher von Braun Kathleen Carley Harold Chestnut Wolt Fabrycky Barbara Grosz Arthur David Hall III Derek Hitchins Robert E. Machol Radhika Nagpal Simon Ramo Joseph Francis Shea Katia Sycara Manuela M. Veloso John N. Warfield
Related fields	Control engineering Computer engineering Industrial engineering Operations research Project management Quality management Risk management Software engineering
Category

v t e Computer science
Note: This template roughly follows the 2012 ACM Computing Classification System.
Hardware	Printed circuit board Peripheral Integrated circuit Very Large Scale Integration Systems on Chip (SoCs) Energy consumption (Green computing) Electronic design automation Hardware acceleration Processor Size / Form
Computer systems organization	Computer architecture Computational complexity Dependability Embedded system Real-time computing
Networks	Network architecture Network protocol Network components Network scheduler Network performance evaluation Network service
Software organization	Interpreter Middleware Virtual machine Operating system Software quality
Software notations and tools	Programming paradigm Programming language Compiler Domain-specific language Modeling language Software framework Integrated development environment Software configuration management Software library Software repository
Software development	Control variable Software development process Requirements analysis Software design Software construction Software deployment Software engineering Software maintenance Programming team Open-source model
Theory of computation	Model of computation Formal language Automata theory Computability theory Computational complexity theory Logic Semantics
Algorithms	Algorithm design Analysis of algorithms Algorithmic efficiency Randomized algorithm Computational geometry
Mathematics of computing	Discrete mathematics Probability Statistics Mathematical software Information theory Mathematical analysis Numerical analysis Theoretical computer science
Information systems	Database management system Information storage systems Enterprise information system Social information systems Geographic information system Decision support system Process control system Multimedia information system Data mining Digital library Computing platform Digital marketing World Wide Web Information retrieval
Security	Cryptography Formal methods Security hacker Security services Intrusion detection system Hardware security Network security Information security Application security
Human–computer interaction	Interaction design Social computing Ubiquitous computing Visualization Accessibility
Concurrency	Concurrent computing Parallel computing Distributed computing Multithreading Multiprocessing
Artificial intelligence	Natural language processing Knowledge representation and reasoning Computer vision Automated planning and scheduling Search methodology Control method Philosophy of artificial intelligence Distributed artificial intelligence
Machine learning	Supervised learning Unsupervised learning Reinforcement learning Multi-task learning Cross-validation
Graphics	Animation Rendering Photograph manipulation Graphics processing unit Mixed reality Virtual reality Image compression Solid modeling
Applied computing	Quantum Computing E-commerce Enterprise software Computational mathematics Computational physics Computational chemistry Computational biology Computational social science Computational engineering Differentiable computing Computational healthcare Digital art Electronic publishing Cyberwarfare Electronic voting Video games Word processing Operations research Educational technology Document management
Category Outline Glossaries

v t e Data structures
Types	Collection Container
Abstract	Associative array Multimap Retrieval Data Structure List Stack Queue Double-ended queue Priority queue Double-ended priority queue Set Multiset Disjoint-set
Arrays	Bit array Circular buffer Dynamic array Hash table Hashed array tree Sparse matrix
Linked	Association list Linked list Skip list Unrolled linked list XOR linked list
Trees	B-tree Binary search tree AA tree AVL tree Red–black tree Self-balancing tree Splay tree Heap Binary heap Binomial heap Fibonacci heap R-tree R* tree R+ tree Hilbert R-tree Trie Hash tree
Graphs	Binary decision diagram Directed acyclic graph Directed acyclic word graph
List of data structures

v t e Tree data structures
Search trees (dynamic sets/associative arrays)	2–3 2–3–4 AA (a,b) AVL B B+ B* B^x (Optimal) Binary search Dancing HTree Interval Order statistic (Left-leaning) Red–black Scapegoat Splay T Treap UB Weight-balanced
Heaps	Binary Binomial Brodal d-ary Fibonacci Leftist Pairing Skew binomial Skew van Emde Boas Weak
Tries	Ctrie C-trie (compressed ADT) Hash Radix Suffix Ternary search X-fast Y-fast
Spatial data partitioning trees	Ball BK BSP Cartesian Hilbert R k-d (implicit k-d) M Metric MVP Octree PH Priority R Quad R R+ R* Segment VP X
Other trees	Cover Exponential Fenwick Finger Fractal tree index Fusion Hash calendar iDistance K-ary Left-child right-sibling Link/cut Log-structured merge Merkle PQ Range SPQR Top

v t e Parsing algorithms
Top-down	Earley LL Recursive descent Tail recursive
Bottom-up	Precedence Simple Operator Shunting-yard LR Simple Look-ahead Canonical Generalized CYK Recursive ascent Shift-reduce
Mixed, other	Combinator Chart Left corner Statistical
Related topics	PEG Definite clause grammar Deterministic parsing Dynamic programming Memoization Parser generator LALR Parse tree AST Scannerless parsing History of compiler construction Comparison of parser generators Operator-precedence grammar

v t e Sorting algorithms
Theory	Computational complexity theory Big O notation Total order Lists Inplacement Stability Comparison sort Adaptive sort Sorting network Integer sorting X + Y sorting Transdichotomous model Quantum sort
Exchange sorts	Bubble sort Cocktail shaker sort Odd–even sort Comb sort Gnome sort Proportion extend sort Quicksort
Selection sorts	Selection sort Heapsort Smoothsort Cartesian tree sort Tournament sort Cycle sort Weak-heap sort
Insertion sorts	Insertion sort Shellsort Splaysort Tree sort Library sort Patience sorting
Merge sorts	Merge sort Cascade merge sort Oscillating merge sort Polyphase merge sort
Distribution sorts	American flag sort Bead sort Bucket sort Burstsort Counting sort Interpolation sort Pigeonhole sort Proxmap sort Radix sort Flashsort
Concurrent sorts	Bitonic sorter Batcher odd–even mergesort Pairwise sorting network Samplesort
Hybrid sorts	Block merge sort Kirkpatrick–Reisch sort Timsort Introsort Spreadsort Merge-insertion sort
Other	Topological sorting Pre-topological order Pancake sorting Spaghetti sort
Impractical sorts	Stooge sort Slowsort Bogosort

v t e Strings
String metric	Approximate string matching Bitap algorithm Damerau–Levenshtein distance Edit distance Gestalt pattern matching Hamming distance Jaro–Winkler distance Lee distance Levenshtein automaton Levenshtein distance Wagner–Fischer algorithm
String-searching algorithm	Apostolico–Giancarlo algorithm Boyer–Moore string-search algorithm Boyer–Moore–Horspool algorithm Knuth–Morris–Pratt algorithm Rabin–Karp algorithm Raita algorithm Trigram search Two-way string-matching algorithm Zhu–Takaoka string matching algorithm
Multiple string searching	Aho–Corasick Commentz-Walter algorithm
Regular expression	Comparison of regular-expression engines Regular grammar Thompson's construction Nondeterministic finite automaton
Sequence alignment	BLAST Hirschberg's algorithm Needleman–Wunsch algorithm Smith–Waterman algorithm
Data structure	DAFSA Suffix array Suffix automaton Suffix tree Generalized suffix tree Rope Ternary search tree Trie
Other	Parsing Pattern matching Compressed pattern matching Longest common subsequence Longest common substring Sequential pattern mining Sorting String rewriting systems String operations

Machine learning and data mining
Part of a series on
Paradigms Supervised learning Unsupervised learning Online learning Batch learning Meta-learning Semi-supervised learning Self-supervised learning Reinforcement learning Curriculum learning Rule-based learning Quantum machine learning
Problems Classification Generative modeling Regression Clustering Dimensionality reduction Density estimation Anomaly detection Data cleaning AutoML Association rules Semantic analysis Structured prediction Feature engineering Feature learning Learning to rank Grammar induction Ontology learning Multimodal learning
Supervised learning (classification • regression) Apprenticeship learning Decision trees Ensembles Bagging Boosting Random forest k-NN Linear regression Naive Bayes Artificial neural networks Logistic regression Perceptron Relevance vector machine (RVM) Support vector machine (SVM)
Clustering BIRCH CURE Hierarchical k-means Fuzzy Expectation–maximization (EM) DBSCAN OPTICS Mean shift
Dimensionality reduction Factor analysis CCA ICA LDA NMF PCA PGD t-SNE SDL
Structured prediction Graphical models Bayes net Conditional random field Hidden Markov
Anomaly detection RANSAC k-NN Local outlier factor Isolation forest
Artificial neural network Autoencoder Cognitive computing Deep learning DeepDream Feedforward neural network Recurrent neural network LSTM GRU ESN reservoir computing Restricted Boltzmann machine GAN Diffusion model SOM Convolutional neural network U-Net Transformer Vision Mamba Spiking neural network Memtransistor Electrochemical RAM (ECRAM)
Reinforcement learning Q-learning SARSA Temporal difference (TD) Multi-agent Self-play
Learning with humans Active learning Crowdsourcing Human-in-the-loop RLHF
Model diagnostics Coefficient of determination Confusion matrix Learning curve ROC curve
Mathematical foundations Kernel machines Bias–variance tradeoff Computational learning theory Empirical risk minimization Occam learning PAC learning Statistical learning VC theory
Machine-learning venues ECML PKDD NeurIPS ICML ICLR IJCAI ML JMLR
Related articles Glossary of artificial intelligence List of datasets for machine-learning research List of datasets in computer vision and image processing Outline of machine learning
v t e

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[edit]

Program analysis

Key concepts

Semantics

Types	Axiomatic Denotational Categorical semantics Operational Big-step Small-step
Models	Lambda calculus Petri net Process calculus Rewriting system State machine Turing machine

Analyses

Static	Abstract interpretation Alias Control flow kCFA Data-flow Dependence Effect system Escape Model checking Pointer Shape Symbolic execution Termination Type systems Typestate
Dynamic	Data-flow Taint tracking Concolic execution Fuzzing Invariant inference Program slicing Testing

Formal methods

Concepts

Logics

Data structures

Tools

Constraint solvers	CHC SAT SMT
Lightweight	Alloy TLA+
Proof assistants	ACL2 Agda Coq F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Twelf

v t e Application binary interface (ABI)
Parts and conventions	Alignment Calling convention Call stack Library static Machine code Memory segmentation Name mangling Object code Opaque pointer Position-independent code Relocation System call Virtual method table
Related topics	Binary-code compatibility Foreign function interface Language binding Linker dynamic Loader Year 2038 problem

v t e Complexity classes
Considered feasible	DLOGTIME AC⁰ ACC⁰ TC⁰ L SL RL FL NL NL-complete NC SC CC P P-complete ZPP RP BPP BQP APX FP
Suspected infeasible	UP NP NP-complete NP-hard co-NP co-NP-complete TFNP FNP AM QMA PH ⊕P PP #P #P-complete IP PSPACE PSPACE-complete
Considered infeasible	EXPTIME NEXPTIME EXPSPACE 2-EXPTIME ELEMENTARY PR R RE ALL
Class hierarchies	Polynomial hierarchy Exponential hierarchy Grzegorczyk hierarchy Arithmetical hierarchy Boolean hierarchy
Families of classes	DTIME NTIME DSPACE NSPACE Probabilistically checkable proof Interactive proof system
List of complexity classes

Data compression methods

Lossless

Entropy type	Adaptive coding Arithmetic Asymmetric numeral systems Golomb Huffman Adaptive Canonical Modified Range Shannon Shannon–Fano Shannon–Fano–Elias Tunstall Unary Universal Exp-Golomb Fibonacci Gamma Levenshtein
Dictionary type	Byte pair encoding Lempel–Ziv 842 LZ4 LZJB LZO LZRW LZSS LZW LZWL Snappy
Other types	BWT CTW CM Delta Incremental DMC DPCM Grammar Re-Pair Sequitur LDCT MTF PAQ PPM RLE
Hybrid	LZ77 + Huffman Deflate LZX LZS LZ77 + ANS LZFSE LZ77 + Huffman + ANS Zstandard LZ77 + Huffman + context Brotli LZSS + Huffman LHA/LZH LZ77 + Range LZMA LZHAM RLE + BWT + MTF + Huffman bzip2

Lossy

Transform type	Discrete cosine transform DCT MDCT DST FFT Wavelet Daubechies DWT SPIHT
Predictive type	DPCM ADPCM LPC ACELP CELP LAR LSP WLPC Motion Compensation Estimation Vector Psychoacoustic

Audio

Concepts	Bit rate ABR CBR VBR Companding Convolution Dynamic range Latency Nyquist–Shannon theorem Sampling Silence compression Sound quality Speech coding Sub-band coding
Codec parts	A-law μ-law DPCM ADPCM DM FT FFT LPC ACELP CELP LAR LSP WLPC MDCT Psychoacoustic model

Image

Concepts	Chroma subsampling Coding tree unit Color space Compression artifact Image resolution Macroblock Pixel PSNR Quantization Standard test image Texture compression
Methods	Chain code DCT Deflate Fractal KLT LP RLE Wavelet Daubechies DWT EZW SPIHT

Video

Concepts	Bit rate ABR CBR VBR Display resolution Frame Frame rate Frame types Interlace Video characteristics Video quality
Codec parts	DCT DPCM Deblocking filter Lapped transform Motion Compensation Estimation Vector Wavelet Daubechies DWT

Theory

Community

Hutter Prize

People

Mark Adler

v t e Computational hardness assumptions
Number theoretic	Integer factorization Phi-hiding RSA problem Strong RSA Quadratic residuosity Decisional composite residuosity Higher residuosity
Group theoretic	Discrete logarithm Diffie-Hellman Decisional Diffie–Hellman Computational Diffie–Hellman
Pairings	External Diffie–Hellman Sub-group hiding Decision linear
Lattices	Shortest vector problem (gap) Closest vector problem (gap) Learning with errors Ring learning with errors Short integer solution
Non-cryptographic	Exponential time hypothesis Unique games conjecture Planted clique conjecture

v t e Types of computer language
Types	Architecture description Data exchange Hardware description Knowledge representation Markup Modeling Programming language Query Shading Specification Stylesheet Transformation
See also	Category:Lists of computer languages Category:Lists of programming languages List of programming languages by type

Programming paradigms (Comparison by language)

Imperative

Structured	Jackson structures Block-structured Modular Non-structured Procedural Programming in the large and in the small Design by contract Invariant-based Nested function
Object-oriented (comparison, list)	Class-based, Prototype-based, Object-based Agent Immutable object Persistent Uniform Function Call Syntax

Declarative

Functional (comparison)	Recursive Anonymous function (Partial application) Higher-order Purely functional Total Strict GADTs Dependent types Functional logic Point-free style Expression-oriented Applicative, Concatenative Function-level, Value-level
Dataflow	Flow-based Reactive (Functional reactive) Signals Streams Synchronous
Logic	Abductive logic Answer set Constraint (Constraint logic) Inductive logic Nondeterministic Ontology Probabilistic logic Query
DSL	Algebraic modeling Array Automata-based (Action) Command (Spacecraft) Differentiable End-user Grammar-oriented Interface description Language-oriented List comprehension Low-code Modeling Natural language Non-English-based Page description Pipes and filters Probabilistic Quantum Scientific Scripting Set-theoretic Simulation Stack-based System Tactile Templating Transformation (Graph rewriting, Production, Pattern) Visual

Concurrent,
distributed,
parallel

Metaprogramming

Attribute-oriented
Automatic (Inductive)
Dynamic
Extensible
Generic
Homoiconicity
Interactive
Macro (Hygienic)
Metalinguistic abstraction
Multi-stage
Program synthesis (Bayesian, Inferential, by demonstration, by example)
Reflective
Self-modifying code
Symbolic
Template

Separation
of concerns

v t e Data types
Uninterpreted	Bit Byte Trit Tryte Word Bit array
Numeric	Arbitrary-precision or bignum Complex Decimal Fixed point Floating point Reduced precision Minifloat Half precision bfloat16 Single precision Double precision Quadruple precision Octuple precision Extended precision Long double Integer signedness Interval Rational
Pointer	Address physical virtual Reference
Text	Character String null-terminated
Composite	Algebraic data type generalized Array Associative array Class Dependent Equality Inductive Intersection List Object metaobject Option type Product Record or Struct Refinement Set Union tagged
Other	Boolean Bottom type Collection Enumerated type Exception Function type Opaque data type Recursive data type Semaphore Stream Strongly typed identifier Top type Type class Empty type Unit type Void
Related topics	Abstract data type Boxing Data structure Generic Kind metaclass Parametric polymorphism Primitive data type Interface Subtyping Type constructor Type conversion Type system Type theory Variable

v t e Database models
Common models	Flat Hierarchical Dimensional Network Relational Entity–relationship Enhanced Graph Object-oriented Entity–attribute–value
Other models	Multi-dimensional Array Semantic Star schema XML database
Implementations	Flat file Column-oriented Document-oriented Object–relational Deductive Temporal Valid time Transaction time Decision time XML data store Key–value store Ordered Key-Value Store Triplestore

v t e Edsger Dijkstra
Works	A Primer of ALGOL 60 Programming (book) Structured Programming (book) A Discipline of Programming (book) A Method of Programming (book) Predicate Calculus and Program Semantics (book) Selected Writings on Computing: A Personal Perspective (book) A Note on Two Problems in Connexion with Graphs Cooperating Sequential Processes Solution of a Problem in Concurrent Programming Control The Structure of the 'THE'-Multiprogramming System Go To Statement Considered Harmful Notes on Structured Programming The Humble Programmer Programming Considered as a Human Activity How Do We Tell Truths That Might Hurt? On the Role of Scientific Thought Self-stabilizing Systems in Spite of Distributed Control On the Cruelty of Really Teaching Computer Science Selected papers EWD manuscripts
Main research areas	Theoretical computing science Software engineering Systems science Algorithm design Concurrent computing Distributed computing Formal methods Programming methodology Programming language research Program design and development Software architecture Philosophy of computer programming and computing science
Related people	Shlomi Dolev Per Brinch Hansen Tony Hoare Ole-Johan Dahl Leslie Lamport David Parnas Jaap Zonneveld Carel S. Scholten Adriaan van Wijngaarden Niklaus Wirth
Wikiquote

v t e Evolutionary computation
Main Topics	Evolutionary algorithm Evolutionary data mining Evolutionary multimodal optimization Human-based evolutionary computation Interactive evolutionary computation
Algorithms	Cellular evolutionary algorithm Covariance Matrix Adaptation Evolution Strategy (CMA-ES) Cultural algorithm Differential evolution Evolutionary programming Genetic algorithm Genetic programming Gene expression programming Evolution strategy Natural evolution strategy Neuroevolution Learning classifier system
Related techniques	Swarm intelligence Ant colony optimization Bees algorithm Cuckoo search Particle swarm optimization Bacterial Colony Optimization
Metaheuristic methods	Firefly algorithm Harmony search Gaussian adaptation Memetic algorithm
Related topics	Artificial development Artificial intelligence Artificial life Digital organism Evolutionary robotics Fitness function Fitness landscape Fitness approximation Genetic operators Interactive evolutionary computation No free lunch in search and optimization Machine learning Mating pool Program synthesis
Journals	Evolutionary Computation (journal)

Automata theory: formal languages and formal grammars

Chomsky hierarchy	Grammars	Languages	Abstract machines
Type-0 — Type-1 — — — — — Type-2 — — Type-3 — —	Unrestricted (no common name) Context-sensitive Positive range concatenation Indexed — Linear context-free rewriting systems Tree-adjoining Context-free Deterministic context-free Visibly pushdown Regular — Non-recursive	Recursively enumerable Decidable Context-sensitive Positive range concatenation^* Indexed^* — Linear context-free rewriting language Tree-adjoining Context-free Deterministic context-free Visibly pushdown Regular Star-free Finite	Turing machine Decider Linear-bounded PTIME Turing Machine Nested stack Thread automaton restricted Tree stack automaton Embedded pushdown Nondeterministic pushdown Deterministic pushdown Visibly pushdown Finite Counter-free (with aperiodic finite monoid) Acyclic finite

Each category of languages, except those marked by a ^*, is a proper subset of the category directly above it. Any language in each category is generated by a grammar and by an automaton in the category in the same line.

v t e Graph and tree traversal algorithms
Search	α–β pruning A* IDA* LPA* SMA* Best-first search Beam search Bidirectional search Breadth-first search Lexicographic Parallel B* Depth-first search Iterative deepening D* Fringe search Jump point search Monte Carlo tree search SSS*
Shortest path	Bellman–Ford Dijkstra's Floyd–Warshall Johnson's Shortest path faster Yen's
Minimum spanning tree	Borůvka's Kruskal's Prim's Reverse-delete
List of graph search algorithms

Information processing

Information processes

information processes by function	perception attention influence operating communication reasoning learning storing decision-making
information processing abstractions	event processing sign processesing signal processing data processing stream processing agent processing state processing

Information processors

natural	nature as information processing humans as information processing systems society as information processing system
mixed	mixed reality brain–computer interface physical computing human–computer interaction
artificial	processors and processes bio-inspired computing ubiquitous computing artificial brain and mind uploading virtual reality virtual world

Information processing
theories and concepts

in biology	computational and systems biology genetic informatics and cellular computing computational neuroscience and neurocomputing
in cognitive psychology	information processing theory mind and intelligence cognitive informatics and neuroinformatics behavior informatics
in computer science	neural computation computation theory algorithms and information structures computational circuits artificial intelligence
in philosophy	computational theory of mind philosophy of information philosophy of artificial intelligence
interdisciplinary	information theory decision theory systems theory
other	infosphere inforg Decoding the Universe information overload

v t e Inter-process communication
Data exchange among threads in computer programs
Methods	File Memory-mapped file Message passing Message queue and mailbox Named pipe Anonymous pipe Pipe Semaphore Shared memory Signal Sockets Network Unix
Protocols and standards	Apple events COM+ CORBA D-Bus DDS DCE ICE OpenBinder Sun RPC POSIX (various methods) SOAP REST Thrift TIPC XML-RPC
Software libraries and frameworks	D-Bus libevent SIMPL LINX

v t e Memory management
Memory management as a function of an operating system
Hardware	Memory management unit (MMU) Translation lookaside buffer (TLB) Input–output memory management unit (IOMMU)
Virtual memory	Demand paging Memory paging Page table Virtual memory compression
Memory segmentation	Protected mode Real mode Virtual 8086 mode x86 memory segmentation
Memory allocator	dlmalloc Hoard jemalloc libumem mimalloc ptmalloc
Manual memory management	Static memory allocation C dynamic memory allocation new and delete (C++)
Garbage collection	Automatic Reference Counting Boehm garbage collector Cheney's algorithm Concurrent mark sweep collector Finalizer Garbage Garbage-first collector Mark–compact algorithm Reference counting Tracing garbage collection Strong reference Weak reference
Memory safety	Buffer overflow Buffer over-read Dangling pointer Stack overflow
Issues	Fragmentation Memory leak Unreachable memory
Other	Automatic variable International Symposium on Memory Management Region-based memory management
Memory management Virtual memory Automatic memory management Memory management algorithms Memory management software

v t e Number-theoretic algorithms
Primality tests	AKS APR Baillie–PSW Elliptic curve Pocklington Fermat Lucas Lucas–Lehmer Lucas–Lehmer–Riesel Proth's theorem Pépin's Quadratic Frobenius Solovay–Strassen Miller–Rabin
Prime-generating	Sieve of Atkin Sieve of Eratosthenes Sieve of Pritchard Sieve of Sundaram Wheel factorization
Integer factorization	Continued fraction (CFRAC) Dixon's Lenstra elliptic curve (ECM) Euler's Pollard's rho p − 1 p + 1 Quadratic sieve (QS) General number field sieve (GNFS) Special number field sieve (SNFS) Rational sieve Fermat's Shanks's square forms Trial division Shor's
Multiplication	Ancient Egyptian Long Karatsuba Toom–Cook Schönhage–Strassen Fürer's
Euclidean division	Binary Chunking Fourier Goldschmidt Newton-Raphson Long Short SRT
Discrete logarithm	Baby-step giant-step Pollard rho Pollard kangaroo Pohlig–Hellman Index calculus Function field sieve
Greatest common divisor	Binary Euclidean Extended Euclidean Lehmer's
Modular square root	Cipolla Pocklington's Tonelli–Shanks Berlekamp Kunerth
Other algorithms	Chakravala Cornacchia Exponentiation by squaring Integer square root Integer relation (LLL; KZ) Modular exponentiation Montgomery reduction Schoof Trachtenberg system
Italics indicate that algorithm is for numbers of special forms

Optimization: Algorithms, methods, and heuristics

Unconstrained nonlinear

Functions

Gradients

Convergence	Trust region Wolfe conditions
Quasi–Newton	Berndt–Hall–Hall–Hausman Broyden–Fletcher–Goldfarb–Shanno and L-BFGS Davidon–Fletcher–Powell Symmetric rank-one (SR1)
Other methods	Conjugate gradient Gauss–Newton Gradient Mirror Levenberg–Marquardt Powell's dog leg method Truncated Newton

Hessians

Newton's method

Constrained nonlinear

General	Barrier methods Penalty methods
Differentiable	Augmented Lagrangian methods Sequential quadratic programming Successive linear programming

Convex optimization

Convex
minimization

Linear and
quadratic

Interior point	Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar
Basis-exchange	Simplex algorithm of Dantzig Revised simplex algorithm Criss-cross algorithm Principal pivoting algorithm of Lemke

Combinatorial

Paradigms

Graph
algorithms

Minimum spanning tree	Borůvka Prim Kruskal

Shortest path	Bellman–Ford SPFA Dijkstra Floyd–Warshall

Network flows

Metaheuristics
Evolutionary algorithm Hill climbing Local search Parallel metaheuristics Simulated annealing Spiral optimization algorithm Tabu search

Software

v t e Types of programming languages
Level	Machine Assembly Compiled Interpreted Low-level High-level Very high-level Esoteric
Generation	First Second Third Fourth Fifth

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