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		In mathematics and computer science, an algorithm is an method for solving a problem expressed as a finite sequence of instructions. The term “algorithm” is derived from the name of Muḥammad ibn Mūsā al-Khwārizmī (born approximately 780 in Khwarezm, died between 835 and 850), the Persian mathematician, astronomer, geographer, and scholar in the House of Wisdom in Baghdad, from the Khorasan province of present-day Uzbekistan [1] .
Muḥammad ibn Mūsā al-Khwārizmī [2]

General Concepts

• General Setwise Operations
• Iteration
• Pseudorandom Number Generator
• Recursion

Sorting and Searching

• ABDADA
• All shortest Paths
• Alpha-Beta
• B*
• Best-First
• Brute-Force
• Depth-First
• Flood Fill Algorithm
• Iterative Search
• Jamboree
• Monte-Carlo Tree Search
• Move Ordering
• MTD(f)
• NegaC*
• NegaScout
• Parallel Alpha-Beta in Cilk
• Parallel Search
• Principal Variation Search
• Proof-Number Search
• Retrograde Analysis
• Search
• SEE - The Swap Algorithm
• SEX Algorithm
• SOMA Algorithm
• SSS* and Dual*
• UCT
• Young Brothers Wait Concept

Enumeration and Backtracking

• Backtracking
• De Bruijn Sequence Generator
• Traversing Subsets of a Set
• Trial and Error

Mathematical Optimization

• CLOP
• Dynamic Programming
• Evolutionary Algorithms
• Hill Climbing
• Simulated Annealing
• SPSA

Combinatorial

• Bit-Twiddling
• BitScan
• Flipping Mirroring and Rotating
• Kogge-Stone Algorithm
• Parallel Prefix Algorithms
• Population Count

See also

• BCH Hashing
• Data
• Fill Algorithms
• Hash Table
• Learning
• Mathematician
• SIMD and SWAR Techniques
• Space-Time Tradeoff
• Zobrist Hashing

Publications

1960 ...

• Donald E. Knuth (1968 ...). The Art of Computer Programming (TAOCP) ^[3]
  Volume 1 - Fundamental Algorithms (1968)
  Volume 2 - Seminumerical Algorithms (1969)
  Volume 3 - Sorting and Searching (1973)
  Volume 4 - Combinatorial Algorithms in preparation (five fascicles have been published as of April 2009)
  Volume 4A - Enumeration and Backtracking
  Volume 4B - Graph and Network Algorithms
  Volume 4C and possibly 4D - Optimization and Recursion
  Volume 5 - Syntactic Algorithms, planned (as of August 2006, estimated in 2015).

1970 ...

• Niklaus Wirth (1976). Algorithms + Data Structures = Programs.
• Georgy Adelson-Velsky, Vladimir Arlazarov, Mikhail Donskoy (1979). Algorithms of adaptive search. Machine Intelligence 9 (eds. Jean Hayes Michie, Donald Michie and L.I. Mikulich), pp. 373-384. Ellis Horwood, Chichester

1980 ...

• Andrei P. Ershov, Donald Knuth (Eds.) (1981). Algorithms in Modern Mathematics and Computer Science. Proceedings, Urgench, Uzbek SSR, September 16-22, 1979. Lecture Notes in Computer Science, Vol. 122, Springer » Ershov Archive
• Michel Gondran, Michel Minoux, Steven Vajda (1984). Graphs and Algorithms. John Wiley & Sons, google, amazon
• Georgy Adelson-Velsky, Vladimir Arlazarov, Mikhail Donskoy (1988). Algorithms for Games. Springer, amazon.com

1990 ...

• John Tromp (1993). Aspects of Algorithms and Complexity. Ph.D. thesis, University of Amsterdam, advisor Paul Vitányi
• Warren D. Smith, Kevin J. Lang (1994). Values of the merging function and algorithm design as a game. NEC Research Institute, ps
• Leen Ammeraal (1996). Algorithms and Data Structures in C++. Chichester: John Wiley
• Steven Skiena (1998). The Algorithm Design Manual. 2nd Edition 2008
• Harald Prokop (1999). Cache-Oblivious Algorithms. Masters thesis, Department of Electrical Engineering and Computer Science, MIT, pdf

2000 ...

• Donald Knuth (2000). Selected Papers on Analysis of Algorithms. CSLI lecture notes series 102
• R. C. T. Lee, S. S. Tseng, R. C. Chang, Y. T. Tsai (2005). Introduction to the Design and Analysis of Algorithms, a Strategic Approach. McGraw-Hill, amazon
• Jill Cirasella (2006). Classical and Quantum Algorithms for Finding Cycles. slides as pdf
• Sanjoy Dasgupta, Christos H. Papadimitriou, Umesh Vazirani (2006). Algorithms. McGraw-Hill, amazon
• Jacques Bahi, Sylvain Contassot-Vivier, Raphaël Couturier (2007). Parallel Iterative Algorithms: From Sequential to Grid Computing. Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series
• David J. Stracuzzi (2007). Randomized Feature Selection. in Huan Liu, Hiroshi Motoda (eds.) Computational Methods of Feature Selection. CRC Press, pdf
• Steven Skiena (2008). The Algorithm Design Manual. Springer, 2nd Edition
• Kurt Mehlhorn, Peter Sanders (2008). Data Structures and Algorithms: The Basic Toolbox. Springer
• Michel Gondran, Michel Minoux (2008, 2010). Graphs, dioids and semirings - New Models and Algorithms. Springer New York, from google, amazon.com, 2nd edition from alibris.com ^[4]
• Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein (2009). Introduction to Algorithms, 3rd Edition.

2010 ...

• Donald Knuth (2010). Selected Papers on Design of Algorithms. CSLI lecture notes series 191, Cambridge University Press
• Berthold Vöcking et al. (eds.) (2011). Algorithms Unplugged. Springer
• Katja Grace (2013). Algorithmic Progress in Six Domains. Technical report 2013-3, Machine Intelligence Research Institute, Berkeley, CA, pdf, 5 Game Playing, 5.1 Chess, 5.2 Go, 9 Machine Learning

External Links

• Algorithm from Wikipedia
• Muḥammad ibn Mūsā al-Khwārizmī
• Banū Mūsā from Wikipedia
• Algorithm characterizations from Wikipedia
• Analysis of algorithms from Wikipedia
• Big O notation from Wikipedia
• Algorithms - Wikibooks
• Dictionary of Algorithms and Data Structures by Paul E. Black, National Institute of Standards and Technology
• Dictionary of Algorithms and Data Structures from Wikipedia
• The Aggregate Magic Algorithms by Hank Dietz » Bit-Twiddling
• Algorithmic Art by Maarten van Emden
• The Art of Computer Programming from Wikipedia
• Java implementation of algorithms from Norvig and Russell's Artificial Intelligence: A Modern Approach. 3rd edition

Algorithms

• Category:Algorithms from Wikipedia
  Algorithms for calculating variance
  Approximation algorithm from Wikipedia
  Cryptographic hash algorithms
  Divide and conquer algorithm
• List of algorithms from Wikipedia
  Deterministic algorithm
  Distributed algorithms
  Nondeterministic algorithm
  Metaheuristic
  Parallel algorithm
  Quantum algorithm
• Randomized algorithm from Wikipedia
  Las Vegas algorithm
  Monte Carlo algorithm
  Pseudorandom number generator

Algebra and Calculus

• Algorism from Wikipedia
• Berlekamp's algorithm from Wikipedia » Elwyn Berlekamp
• Berlekamp–Massey algorithm from Wikipedia
• Buchberger's algorithm from Wikipedia
• Cantor–Zassenhaus algorithm from Wikipedia
• Computus from Wikipedia
• Divisibility rule from Wikipedia
• Division (digital) from Wikipedia
• Euclidean algorithm from Wikipedia
• Gaussian elimination from Wikipedia
• Gauss–Newton algorithm from Wikipedia
• Householder's method from Wikipedia
• Kuwaiti algorithm from Wikipedia
• Levenberg–Marquardt algorithm from Wikipedia
• Multiplication algorithm from Wikipedia
  Karatsuba algorithm from Wikipedia
  Algorithms: Design and Analysis, Part 1 by Tim Roughgarden, Stanford University, Coursera, YouTube Video
  
• Numerical analysis from Wikipedia
• Numerical linear algebra from Wikipedia
• Pollard's kangaroo algorithm from Wikipedia
• Quine–McCluskey algorithm from Wikipedia
• Rod calculus from Wikipedia
• Root-finding algorithm from Wikipedia

Graphics

• Even-odd rule from Wikipedia
• Flood fill from Wikipedia
• Line drawing algorithm from Wikipedia
  Digital Differential Analyzer (graphics algorithm)
  Bresenham's line algorithm
  Xiaolin Wu's line algorithm
• Ray tracing (graphics) from Wikipedia
• Spline interpolation from Wikipedia
  De Boor's algorithm
  De Casteljau's algorithm

Linear Programming

• Criss-cross algorithm from Wikipedia
• Karmarkar's algorithm from Wikipedia
• Simplex algorithm from Wikipedia

Sorting and Searching

• Merge algorithm from Wikipedia
• Search algorithm from Wikipedia
  A* from Wikipedia
  Bellman–Ford algorithm
  Dijkstra's algorithm
  Flooding algorithm
  Floyd–Warshall algorithm
  Greedy algorithm
  Hill climbing
  Kruskal's algorithm
  Nearest neighbour algorithm
  String searching algorithm
• Sorting algorithm from Wikipedia

Complexity

• Category: Computational complexity theory from Wikipedia
• Combinatorial explosion from Wikipedia
• Complexity from Wikipedia
• Complexity class from Wikipedia
• Computational Complexity of Games and Puzzles by David Eppstein
• Computational complexity theory from Wikipedia » Algorithms
• Game complexity from Wikipedia » Games
• Go and mathematics from Wikipedia » Go
• List of complexity classes from Wikipedia
• Problem solving from Wikipedia » Artificial Intelligence
• Reduction (complexity) from Wikipedia
• Shannon number from Wikipedia » Claude Shannon
• Time complexity from Wikipedia
• Wheat and chessboard problem from Wikipedia » Chessboard

Misc

• Correctness (disambiguation) from Wikipedia
• Correctness (computer science) from Wikipedia
• Halting problem from Wikipedia
• Kraan - Gut und Richtig (1973), YouTube Video
  

References

1. ^ Kurt Mehlhorn, Peter Sanders (2008). Data Structures and Algorithms: The Basic Toolbox. Springer, Appetizer: Integer Arithmetics (pdf)
2. ^ A stamp issued September 6, 1983 in the Soviet Union, commemorating Al-Khwārizmī's (approximate) 1200th birthday
3. ^ The Art of Computer Programming from Wikipedia
4. ^ Ordinal optimization from Wikipedia

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