Algorithmic technique

In mathematics and computer science, an algorithmic technique[1] is a general approach for implementing a process or computation.[2]

General techniques

There are several broadly recognized algorithmic techniques that offer a proven method or process for designing and constructing algorithms. Different techniques may be used depending on the objective, which may include searching, sorting, mathematical optimization, constraint satisfaction, categorization, analysis, and prediction.[3]

Brute force

Brute force is a simple, exhaustive technique that evaluates every possible outcome to find a solution.[4]

Divide and conquer

The divide and conquer technique decomposes complex problems recursively into smaller sub-problems. Each sub-problem is then solved and these partial solutions are recombined to determine the overall solution. This technique is often used for searching and sorting.[5]

Dynamic

Dynamic programming is a systematic technique in which a complex problem is decomposed recursively into smaller, overlapping subproblems for solution. Dynamic programming stores the results of the overlapping sub-problems locally using an optimization technique called memoization.[6]

Evolutionary

An evolutionary approach develops candidate solutions and then, in a manner similar to biological evolution, performs a series of random alterations or combinations of these solutions and evaluates the new results against a fitness function. The most fit or promising results are selected for additional iterations, to achieve an overall optimal solution.[7]

Graph traversal

Graph traversal is a technique for finding solutions to problems that can be represented as graphs. This approach is broad, and includes depth-first search, breadth-first search, tree traversal, and many specific variations that may include local optimizations and excluding search spaces that can be determined to be non-optimum or not possible. These techniques may be used to solve a variety of problems including shortest path and constraint satisfaction problems.[8]

Greedy

A greedy approach begins by evaluating one possible outcome from the set of possible outcomes, and then searches locally for an improvement on that outcome. When a local improvement is found, it will repeat the process and again search locally for additional improvements near this local optimum. A greedy technique is generally simple to implement, and these series of decisions can be used to find local optimums depending on where the search began. However, greedy techniques may not identify the global optimum across the entire set of possible outcomes.,[9]

Heuristic

A heuristic approach employs a practical method to reach an immediate solution not guaranteed to be optimal.[10]

Learning

Learning techniques employ statistical methods to perform categorization and analysis without explicit programming. Supervised learning, unsupervised learning, reinforcement learning, and deep learning techniques are included in this category.[11]

Mathematical optimization

Mathematical optimization is a technique that can be used to calculate a mathematical optimum by minimizing or maximizing a function.[12]

Modeling

Modeling is a general technique for abstracting a real-world problem into a framework or paradigm that assists with solution.[13]

Recursion

Recursion is a general technique for designing a algorithm that calls itself with a progressively simpler part of the task down to one or more base cases with defined results.[14][15]

See also

Notes
  1. "technique | Definition of technique in English by Oxford Dictionaries". Oxford Dictionaries | English. Retrieved 2019-03-23.
  2. Cormen, Thomas H.; Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford (2001). Introduction To Algorithms. MIT Press. p. 9. ISBN 9780262032933.
  3. Skiena, Steven S. (1998). The Algorithm Design Manual: Text. Springer Science & Business Media. ISBN 9780387948607.
  4. "What is brute force? Webopedia Definition". www.webopedia.com. Retrieved 2019-03-23.
  5. Bentley, Jon Louis; Shamos, Michael Ian (1976). "Divide-and-conquer in Multidimensional Space". Proceedings of the Eighth Annual ACM Symposium on Theory of Computing. STOC '76. New York, NY, USA: ACM: 220–230. doi:10.1145/800113.803652.
  6. Bellman, Richard (1966-07-01). "Dynamic Programming". Science. 153 (3731): 34–37. doi:10.1126/science.153.3731.34. ISSN 0036-8075. PMID 17730601.
  7. Coello Coello, Carlos A. (1999-08-01). "A Comprehensive Survey of Evolutionary-Based Multiobjective Optimization Techniques". Knowledge and Information Systems. 1 (3): 269–308. doi:10.1007/BF03325101. ISSN 0219-3116.
  8. Kumar, Nitin; Wayne, Kevin (2014-02-01). Algorithms. Addison-Wesley Professional. ISBN 9780133799101.
  9. "greedy algorithm". xlinux.nist.gov. Retrieved 2019-03-23.
  10. "heuristic". xlinux.nist.gov. Retrieved 2019-03-23.
  11. Witten, Ian H.; Frank, Eibe; Hall, Mark A.; Pal, Christopher J. (2016-10-01). Data Mining: Practical Machine Learning Tools and Techniques. Morgan Kaufmann. ISBN 9780128043578.
  12. Marler, R.T.; Arora, J.S. (2004-04-01). "Survey of multi-objective optimization methods for engineering". Structural and Multidisciplinary Optimization. 26 (6): 369–395. doi:10.1007/s00158-003-0368-6. ISSN 1615-1488.
  13. Skiena, Steven S. (1998). The Algorithm Design Manual: Text. Springer Science & Business Media. ISBN 9780387948607.
  14. "recursion". xlinux.nist.gov. Retrieved 2019-03-23.
  15. "Programming - Recursion". www.cs.utah.edu. Retrieved 2019-03-23.
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