Outline of algorithms

The following outline is provided as an overview of and topical guide to algorithms:

An algorithm is a finite, well-defined sequence of instructions or rules for solving a problem or performing a computation.^[1] Algorithms are central to computer science, mathematics, operations research, artificial intelligence,^[2] cryptography, data compression, computer graphics, bioinformatics, and many other fields.^[3] The study of algorithms includes their design, proof of correctness, efficiency, computational complexity, and implementation in computer programs.^[4]^[5]

Nature of algorithms

Algorithm — finite sequence of instructions for solving a problem or performing a computation
Computer program — implementation of algorithms and data-processing instructions in a programming language
Data structure — organization of data used by algorithms
Heuristic — practical problem-solving method that may not guarantee an optimal solution
Pseudocode — informal notation for describing algorithms
Specification — formal or informal statement of what an algorithm is intended to do
State — stored information used during a computation
Termination analysis — study of whether an algorithm eventually halts
Turing machine — mathematical model of computation used in computability theory

History of algorithms

Euclidean algorithm — ancient algorithm for computing the greatest common divisor
Muhammad ibn Musa al-Khwarizmi — mathematician whose Latinized name is associated with the word algorithm
Algorithmic logic — logic-based study of programs and algorithms
Computability theory — study of what can be computed
Church–Turing thesis — thesis concerning the nature of effective computation
Turing machine — model formalizing computation
Lambda calculus — formal system used in the study of computation
Von Neumann architecture — computer architecture influencing practical algorithm implementation

Algorithm analysis

Analysis of algorithms — study of the correctness and efficiency of algorithms
Asymptotic analysis — analysis of algorithm behavior as input size grows
Big O notation — upper-bound notation for growth rates
Big Omega notation — lower-bound notation for growth rates
Big Theta notation — tight-bound notation for growth rates
Time complexity — amount of time an algorithm uses as input size changes
Space complexity — amount of memory an algorithm uses as input size changes
Best, worst and average case — common forms of algorithm-performance analysis
Amortized analysis — analysis of average cost over a sequence of operations
Competitive analysis (online algorithm) — analysis of online algorithms compared with optimal offline algorithms
Correctness (computer science) — property that an algorithm satisfies its specification
Loop invariant — condition used to prove correctness of iterative algorithms
Recurrence relation — equation often used to analyze recursive algorithms
Master theorem (analysis of algorithms) — theorem for solving many divide-and-conquer recurrences

Algorithm design paradigms

Brute-force search — method of exhaustively checking candidate solutions
Divide-and-conquer algorithm — technique that divides a problem into smaller subproblems
Decrease and conquer — technique that reduces a problem to a smaller instance
Dynamic programming — technique for solving problems with overlapping subproblems and optimal substructure
Greedy algorithm — algorithm that makes locally optimal choices
Backtracking — search technique that abandons partial solutions that cannot lead to valid solutions
Branch and bound — search technique using bounds to eliminate candidate solutions
Randomized algorithm — algorithm using randomness as part of its logic
Approximation algorithm — algorithm that finds near-optimal solutions for hard optimization problems
Online algorithm — algorithm that receives input incrementally
Parallel algorithm — algorithm designed for parallel computation
Distributed algorithm — algorithm designed for distributed systems
Streaming algorithm — algorithm for processing data streams with limited memory
Quantum algorithm — algorithm designed for quantum computers^[6]

Data structures and related algorithms

Arrays, lists, and sequences

Trees

Hashing and sets

Graph data structures

Operating system and memory-management algorithms

Searching algorithms

Sorting and order statistics

Comparison sorting

Non-comparison sorting

Order statistics

Graph algorithms

Graph traversal

Shortest paths

Spanning trees and connectivity

Network flow and matching

Graph coloring and hard graph problems

String algorithms

Numerical and mathematical algorithms

Arithmetic and number theory

Linear algebra

Numerical optimization and approximation

Optimization algorithms

Artificial intelligence and machine learning algorithms

Search and planning

Supervised learning

Unsupervised learning

Reinforcement learning

Algorithmic gameplay

AI-assisted algorithm discovery

Cryptographic algorithms

Symmetric-key algorithms

Public-key algorithms

Hashing and authentication

Compression algorithms

Lossless compression

Lossy compression techniques

Computational geometry algorithms

Computer graphics and image-processing algorithms

Database and information retrieval algorithms

Distributed, concurrent, and networking algorithms

Distributed systems

Concurrency

Networking

Bioinformatics and scientific algorithms

Complexity classes and algorithmic limits

Lists of algorithms

Notable people

Cryptography and randomized algorithms

Whitfield Diffie — Diffie–Hellman key exchange
Martin Hellman — Diffie–Hellman key exchange
Ron Rivest — RSA and cryptographic algorithms
Adi Shamir — RSA and cryptographic algorithms
Leonard Adleman — RSA and DNA computing
Shafi Goldwasser — cryptography and computational complexity

Artificial intelligence and search algorithms

John McCarthy — artificial intelligence and symbolic artificial intelligence
Marvin Minsky — artificial intelligence and computational models
Herbert A. Simon — heuristic search and artificial intelligence
Allen Newell — heuristic search and artificial intelligence
Arthur Samuel — early machine learning and game-playing algorithms
Judea Pearl — Bayesian networks and probabilistic reasoning

References

^ "Algorithm". Encyclopædia Britannica. Retrieved May 4, 2026.
^ "Artificial intelligence (AI) algorithms: a complete overview". Tableau. Retrieved May 5, 2026.
^ "Computer science - Algorithms and complexity". Encyclopædia Britannica. Retrieved May 4, 2026.
^ "Analysis of algorithms". Encyclopædia Britannica. Retrieved May 4, 2026.
^ "What is an Algorithm | Introduction to Algorithms". GeeksforGeeks. December 20, 2025. Retrieved May 5, 2026.
^ "Algorithms Design Techniques". GeeksforGeeks. July 28, 2025. Retrieved May 5, 2026.

External links

Media related to Algorithms at Wikimedia Commons
Algorithms at Wikibooks
Learning materials related to Topic:Algorithms at Wikiversity

[britannica-algorithm-1] "Algorithm". Encyclopædia Britannica. Retrieved May 4, 2026.

[2] "Artificial intelligence (AI) algorithms: a complete overview". Tableau. Retrieved May 5, 2026.

[britannica-computer-science-3] "Computer science - Algorithms and complexity". Encyclopædia Britannica. Retrieved May 4, 2026.

[britannica-analysis-4] "Analysis of algorithms". Encyclopædia Britannica. Retrieved May 4, 2026.

[5] "What is an Algorithm | Introduction to Algorithms". GeeksforGeeks. December 20, 2025. Retrieved May 5, 2026.

[6] "Algorithms Design Techniques". GeeksforGeeks. July 28, 2025. Retrieved May 5, 2026.

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v t e Data structures and algorithms
Data structures	Array Associative array Binary search tree Fenwick tree Graph Hash table Heap Linked list Queue Segment tree Stack String Tree Trie
Algorithms and algorithmic paradigms	Backtracking Binary search Breadth-first search Brute-force search Depth-first search Divide and conquer Dynamic programming Graph traversal Fold Greedy Hash function Minimax Online Randomized Recursion Root-finding Sorting Streaming Sweep line String-searching Topological sorting
List of data structures List of algorithms