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.⁴⁵

• 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

• 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

• 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

• 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 computers⁶

• Array (data structure)
• Linked list
• Dynamic array
• Stack (abstract data type)
• Queue (abstract data type)
• Deque
• Priority queue
• Circular buffer

• Tree (data structure)
• Binary tree
• Binary search tree
• AVL tree
• Red–black tree
• B-tree
• B+ tree
• Trie
• Segment tree
• Fenwick tree
• Heap (data structure)

• Hash table
• Hash function
• Bloom filter
• Disjoint-set data structure
• Union–find algorithm
• Locality-sensitive hashing

• Graph (abstract data type)
• Adjacency list
• Adjacency matrix
• Incidence matrix

• Scheduling algorithms
• Round-robin scheduling
• Shortest job next
• Rate-monotonic scheduling
• Earliest deadline first scheduling
• Page replacement algorithm
• Least recently used
• Cache replacement policies

• Linear search
• Binary search algorithm
• Interpolation search
• Exponential search
• Jump search
• Depth-first search
• Breadth-first search
• Best-first search
• Beam search
• A* search algorithm
• Dijkstra's algorithm
• Iterative deepening depth-first search
• Monte Carlo tree search

• Bubble sort
• Insertion sort
• Selection sort
• Merge sort
• Quicksort
• Heapsort
• Timsort
• Introsort
• Shellsort
• Tree sort

• Counting sort
• Radix sort
• Bucket sort
• Pigeonhole sort

• Selection algorithm
• Quickselect
• Median of medians
• Order statistic tree

• Depth-first search
• Breadth-first search
• Topological sorting
• Flood fill

• Dijkstra's algorithm
• Bellman–Ford algorithm
• Floyd–Warshall algorithm
• Johnson's algorithm
• A* search algorithm

• Minimum spanning tree
• Kruskal's algorithm
• Prim's algorithm
• Borůvka's algorithm
• Connected component (graph theory)
• Strongly connected component
• Tarjan's strongly connected components algorithm

• Maximum flow problem
• Ford–Fulkerson algorithm
• Edmonds–Karp algorithm
• Push–relabel maximum flow algorithm
• Minimum-cost flow problem
• Bipartite matching
• Hopcroft–Karp algorithm
• Blossom algorithm

• Graph coloring
• Clique problem
• Independent set (graph theory)
• Hamiltonian path problem
• Travelling salesman problem

• String-searching algorithm
• Knuth–Morris–Pratt algorithm
• Boyer–Moore string-search algorithm
• Rabin–Karp algorithm
• Aho–Corasick algorithm
• Levenshtein distance
• Edit distance
• Longest common subsequence
• Longest common substring
• Suffix tree
• Suffix array
• Burrows–Wheeler transform
• Regular expression
• Parsing
• Earley parser
• CYK algorithm

• Euclidean algorithm
• Extended Euclidean algorithm
• Sieve of Eratosthenes
• Integer factorization
• Primality test
• AKS primality test
• Modular exponentiation
• Fast Fourier transform
• Karatsuba algorithm
• Schönhage–Strassen algorithm

• Gaussian elimination
• LU decomposition
• QR decomposition
• Singular value decomposition
• Eigenvalue algorithm
• Strassen algorithm
• Matrix chain multiplication

• Newton's method
• Gradient descent
• Conjugate gradient method
• Simulated annealing
• Expectation–maximization algorithm
• Numerical integration
• Monte Carlo method

• Linear programming
• Simplex algorithm
• Interior-point method
• Integer programming
• Dynamic programming
• Gradient descent
• Stochastic gradient descent
• Newton's method
• Quasi-Newton method
• Broyden–Fletcher–Goldfarb–Shanno algorithm
• Lagrange multiplier
• Constraint satisfaction problem
• Local search (optimization)
• Hill climbing
• Tabu search
• Genetic algorithm
• Ant colony optimization algorithms
• Particle swarm optimization
• Evolutionary algorithm

• A* search algorithm
• Minimax
• Alpha–beta pruning
• Graphplan
• Monte Carlo tree search
• Automated planning and scheduling
• Constraint satisfaction problem

• Linear regression
• Logistic regression
• Decision tree learning
• Random forest
• Support vector machine
• k-nearest neighbors algorithm
• Naive Bayes classifier
• Gradient boosting
• Artificial neural network
• Backpropagation

• Cluster analysis
• K-means clustering
• Hierarchical clustering
• Principal component analysis
• Independent component analysis
• Autoencoder
• Self-organizing map

• Reinforcement learning
• Q-learning
• State–action–reward–state–action (SARSA)
• Temporal difference learning
• Policy gradient method
• Actor–critic algorithm
• Deep reinforcement learning

• AlphaGo
• AlphaGo Zero
• AlphaZero
• MuZero
• TD-Gammon
• Chinook (draughts player)
• Deep Blue (chess computer)

• AlphaDev
• AlphaEvolve
• AlphaTensor
• Neural architecture search
• Automated machine learning
• Program synthesis

• Advanced Encryption Standard
• Data Encryption Standard
• Triple DES
• Blowfish (cipher)
• Twofish
• ChaCha20-Poly1305

• RSA cryptosystem
• Diffie–Hellman key exchange
• Elliptic-curve cryptography
• Digital Signature Algorithm
• EdDSA

• Cryptographic hash function
• MD5
• SHA-1
• SHA-2
• SHA-3
• Hash-based message authentication code
• Password-based key derivation function
• Bcrypt
• Argon2

• Huffman coding
• Arithmetic coding
• Run-length encoding
• Lempel–Ziv–Welch
• LZ77 and LZ78
• DEFLATE
• Burrows–Wheeler transform

• Transform coding
• Discrete cosine transform
• Modified discrete cosine transform
• Vector quantization
• Quantization
• Motion compensation

• Convex hull algorithms
• Graham scan
• Gift wrapping algorithm
• Delaunay triangulation
• Voronoi diagram
• Line segment intersection
• Point location
• Closest pair of points problem
• Rotating calipers
• Sweep line algorithm

• Bresenham's line algorithm
• Flood fill
• Scanline rendering
• Z-buffering
• Ray casting
• Ray tracing (graphics)
• Path tracing
• Phong shading
• Texture mapping
• Bump mapping
• Normal mapping
• Marching cubes
• Canny edge detector
• Random sample consensus (RANSAC)
• Scale-invariant feature transform
• Hough transform
• Seam carving

• B-tree
• B+ tree
• Hash join
• Sort-merge join
• Query optimization
• PageRank
• Inverted index
• Tf–idf
• BM25
• Locality-sensitive hashing
• MapReduce
• Consistent hashing

• Consensus (computer science)
• Paxos (computer science)
• Raft (algorithm)
• Byzantine fault tolerance
• Vector clock
• Lamport timestamp
• Leader election
• Gossip protocol

• Mutual exclusion
• Semaphore (programming)
• Monitor (synchronization)
• Deadlock prevention algorithms
• Lock-free and wait-free algorithms
• Compare-and-swap

• Routing algorithm
• Dijkstra's algorithm
• Bellman–Ford algorithm
• Distance-vector routing protocol
• Link-state routing protocol
• Congestion control
• Transmission Control Protocol

• Needleman–Wunsch algorithm
• Smith–Waterman algorithm
• BLAST (biotechnology)
• Sequence alignment
• Hidden Markov model
• Viterbi algorithm
• Phylogenetic tree
• Molecular dynamics
• Finite element method
• Fast multipole method

• P (complexity)
• NP (complexity)
• NP-completeness
• NP-hardness
• EXPTIME
• PSPACE
• BPP (complexity)
• BQP
• Undecidable problem
• Halting problem
• Rice's theorem
• No free lunch theorem

• List of algorithms
• List of artificial intelligence algorithms
• List of combinatorial algorithms

• Al-Khwarizmi — namesake of the term algorithm
• Charles Babbage — early computing pioneer
• Ada Lovelace — wrote an early algorithm for the Analytical Engine
• Alan Turing — computability theory and the Turing machine
• Alonzo Church — lambda calculus and computability theory
• John von Neumann — von Neumann architecture and numerical analysis

• Donald Knuth — analysis of algorithms and The Art of Computer Programming
• Edsger W. Dijkstra — Dijkstra's algorithm and structured programming
• Robert W. Floyd — Floyd–Warshall algorithm and algorithm analysis
• Tony Hoare — Quicksort and Hoare logic
• Michael O. Rabin — randomized algorithms and automata theory
• Richard M. Karp — NP-completeness and combinatorial optimization

• Stephen Cook — Cook–Levin theorem and NP-completeness
• Leonid Levin — NP-completeness and computational complexity theory
• Juris Hartmanis — computational complexity theory
• Richard E. Stearns — computational complexity theory
• Avi Wigderson — randomness and computational complexity

• Richard Bellman — dynamic programming and shortest-path algorithms
• George Dantzig — simplex algorithm and linear programming
• Jack Edmonds — matching and polyhedral combinatorics
• L. R. Ford Jr. — Ford–Fulkerson algorithm and maximum flow problems
• D. R. Fulkerson — Ford–Fulkerson algorithm and network flows
• Robert Tarjan — graph algorithms and data structures

• 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

• 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

See also

See also

• Algorithm engineering
• Outline of artificial intelligence
• Outline of computer science
• Procedure (computer science)
• List of data structures
• List of numerical analysis topics
• List of optimization software

References

References

1. "Algorithm". Encyclopædia Britannica. Retrieved May 4, 2026.
2. "Artificial intelligence (AI) algorithms: a complete overview". Tableau. Retrieved May 5, 2026.
3. "Computer science - Algorithms and complexity". Encyclopædia Britannica. Retrieved May 4, 2026.
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.

Further reading

Further reading

• Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford (2022). Introduction to Algorithms (4th ed.). MIT Press. ISBN 978-0-262-04630-5.
• Knuth, Donald E. (1968). The Art of Computer Programming. Addison-Wesley. ISBN 978-0-201-89683-1.
• Kleinberg, Jon; Tardos, Éva (2005). Algorithm Design. Pearson Education. ISBN 978-0-321-29535-4.
• Skiena, Steven S. (2020). The Algorithm Design Manual (3rd ed.). Springer. ISBN 978-3-030-54255-9.

External links

External links

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