Broad definition of the term algorithm
An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.
Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations. With the increasing automation of services, more and more decisions are being made by algorithms. Some general examples are; risk assessments, anticipatory policing, and pattern recognition technology.[1]
The following is a list of well-known algorithms along with one-line descriptions for each.
Automated planning
Combinatorial algorithms
General combinatorial algorithms
Graph algorithms
Graph drawing
Network theory
Routing for graphs
Graph search
Subgraphs
Sequence algorithms
Approximate sequence matching
- Bitap algorithm: fuzzy algorithm that determines if strings are approximately equal.
- Phonetic algorithms
- String metrics: computes a similarity or dissimilarity (distance) score between two pairs of text strings
- Trigram search: search for text when the exact syntax or spelling of the target object is not precisely known
Selection algorithms
Sequence search
Sequence merging
- Simple merge algorithm
- k-way merge algorithm
- Union (merge, with elements on the output not repeated)
Sequence permutations
Sequence combinations
Sequence alignment
Sequence sorting
- Exchange sorts
- Bubble sort: for each pair of indices, swap the items if out of order
- Cocktail shaker sort or bidirectional bubble sort, a bubble sort traversing the list alternately from front to back and back to front
- 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
- 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
- Merge sorts
- Non-comparison sorts
- 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
- Smoothgamersort
- Other
- Unknown class
Subsequences
Substrings
Computational mathematics
Abstract algebra
Computer algebra
Geometry
Number theoretic algorithms
Numerical algorithms
Differential equation solving
Elementary and special functions
Geometric
Interpolation and extrapolation
Linear algebra
Monte Carlo
Numerical integration
Root finding
Optimization algorithms
Hybrid Algorithms
Computational science
Astronomy
Bioinformatics
Geoscience
- Vincenty's formulae: a fast algorithm to calculate the distance between two latitude/longitude points on an ellipsoid
- Geohash: a public domain algorithm that encodes a decimal latitude/longitude pair as a hash string
Linguistics
Medicine
Physics
Statistics
Computer science
Computer architecture
- Tomasulo algorithm: allows sequential instructions that would normally be stalled due to certain dependencies to execute non-sequentially
Computer graphics
- Clipping
- Contour lines and Isosurfaces
- 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.
- Hidden-surface removal or Visual surface determination
- Line Drawing: graphical algorithm for approximating a line segment on discrete graphical media.
- 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
- Binary space partitioning
Cryptography
- Asymmetric (public key) encryption:
- Digital signatures (asymmetric authentication):
- DSA, and its variants:
- RSA
- Cryptographic hash functions (see also the section on message authentication codes):
- BLAKE
- MD5 – Note that there is now a method of generating collisions for MD5
- RIPEMD-160
- SHA-1 – Note that there is now a method of generating collisions for SHA-1
- SHA-2 (SHA-224, SHA-256, SHA-384, SHA-512)
- SHA-3 (SHA3-224, SHA3-256, SHA3-384, SHA3-512, SHAKE128, SHAKE256)
- Tiger (TTH), usually used in Tiger tree hashes
- WHIRLPOOL
- Cryptographically secure pseudo-random number generators
- Key exchange
- Key derivation functions, often used for password hashing and key stretching
- Message authentication codes (symmetric authentication algorithms, which take a key as a parameter):
- Secret sharing, Secret Splitting, Key Splitting, M of N algorithms
- Symmetric (secret key) encryption:
- Post-quantum cryptography
- Proof-of-work algorithms
Digital logic
Machine learning and statistical classification
Programming language theory
Parsing
Quantum algorithms
Theory of computation and automata
Information theory and signal processing
Coding theory
Error detection and correction
Lossless compression algorithms
Lossy compression algorithms
Digital signal processing
Image processing
Software engineering
Database algorithms
Distributed systems algorithms
Memory allocation and deallocation algorithms
Networking
Operating systems algorithms
Process synchronization
Scheduling
I/O scheduling
Disk scheduling
See also
References
- ^ "algorithm". LII / Legal Information Institute. Retrieved 2023-10-26.
- ^ Gegenfurtner, Karl R. (1992-12-01). "PRAXIS: Brent's algorithm for function minimization". Behavior Research Methods, Instruments, & Computers. 24 (4): 560–564. doi:10.3758/BF03203605. ISSN 1532-5970.
- ^ "richardshin.com | Floyd's Cycle Detection Algorithm". 2013-09-30. Retrieved 2023-10-26.
- ^ "Eytzinger Binary Search - Algorithmica". Retrieved 2023-04-09.
- ^ "Shannon-Fano-Elias Coding" (PDF). my.ece.msstate.edu. Archived from the original (PDF) on 2021-02-28. Retrieved 2023-10-11.
- ^ "Archived copy" (PDF). www.vision.ee.ethz.ch. Archived from the original (PDF) on 21 February 2007. Retrieved 13 January 2022.
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: CS1 maint: archived copy as title (link) - ^ "Archived copy" (PDF). Archived from the original (PDF) on 2013-10-06. Retrieved 2013-10-05.
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