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Computer Algorithm
A sequence step algorithm (SQS-AL) is an algorithm implemented in a discrete event simulation system to maximize resource utilization. This is achieved
Sequence_step_algorithm
Finds likely sequence of hidden states
The Viterbi algorithm is a dynamic programming algorithm that finds the most likely sequence of hidden events that would explain a sequence of observed
Viterbi_algorithm
On finding a repeating loop in a sequence
science, cycle detection or cycle finding is the algorithmic problem of finding a cycle in a sequence of iterated function values. For any function f that
Cycle_detection
Simple checksum formula
The Luhn algorithm or Luhn formula (creator: IBM scientist Hans Peter Luhn), also known as the "modulus 10" or "mod 10" algorithm, is a simple check digit
Luhn_algorithm
Sequence of operations for a task
In mathematics and computer science, an algorithm (/ˈælɡərɪðəm/ ) is a finite sequence of mathematically rigorous instructions, typically used to solve
Algorithm
Algorithm for computing greatest common divisors
In mathematics, the Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers
Euclidean_algorithm
Algorithm for shuffling a finite sequence
Fisher–Yates shuffle is an algorithm for shuffling a finite sequence. The algorithm takes a list of all the elements of the sequence, and continually determines
Fisher–Yates_shuffle
Iterative method for finding maximum likelihood estimates in statistical models
next E step. It can be used, for example, to estimate a mixture of gaussians, or to solve the multiple linear regression problem. The EM algorithm was explained
Expectation–maximization algorithm
Expectation–maximization_algorithm
Method for aligning biological sequences
The Needleman–Wunsch algorithm is an algorithm used in bioinformatics to align protein or nucleotide sequences. It was one of the first applications of
Needleman–Wunsch_algorithm
Integer factorization algorithm
known beforehand, this sequence cannot be explicitly computed in the algorithm. Yet in it lies the core idea of the algorithm. Because the number of possible
Pollard's_rho_algorithm
Method of generating all permutations of n objects
generated by Heap's algorithm is the beginning of the sequence of permutations of n+1 objects. So there is one infinite sequence of permutations generated
Heap's_algorithm
Algorithm to be run on quantum computers
(or non-quantum) algorithm is a finite sequence of instructions, or a step-by-step procedure for solving a problem, where each step or instruction can
Quantum_algorithm
conversion between a labeled tree and its Prüfer sequence Tarjan's off-line lowest common ancestors algorithm: computes lowest common ancestors for pairs of
List_of_algorithms
Algorithm for finding shortest paths
Dijkstra's algorithm (/ˈdaɪk.strəz/, DYKE-strəz) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent
Dijkstra's_algorithm
Algorithm for solving a puzzle or game in the fewest possible moves
configurations. To solve the puzzle a sequence of moves is applied, starting from some arbitrary initial configuration. An algorithm can be considered to solve such
God's_algorithm
Algorithm on linear-feedback shift registers
Berlekamp–Massey algorithm is an algorithm that will find the shortest linear-feedback shift register (LFSR) for a given binary output sequence. The algorithm will
Berlekamp–Massey_algorithm
Method for computing the relation of two integers with their greatest common divisor
Euclidean algorithm with a and b as input, consists of computing a sequence q 1 , … , q k {\displaystyle q_{1},\ldots ,q_{k}} of quotients and a sequence r 0
Extended_Euclidean_algorithm
Node ordering for directed acyclic graphs
Topological sorting forms the basis of linear-time algorithms for finding the critical path of the project, a sequence of milestones and tasks that controls the
Topological_sorting
Sequence in computer science
output value in sequence order. However, despite their ease of computation, prefix sums are a useful primitive in certain algorithms such as counting
Prefix_sum
Numbers obtained by adding the two previous ones
Fibonacci sequence is a sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known
Fibonacci_sequence
non-sentinel input weight. The algorithm maintains a sequence of these values, with the two sentinel values at each end. The initial sequence is just the order in
Garsia–Wachs_algorithm
Universal lossless data compression algorithm
compression algorithm created by Abraham Lempel, Jacob Ziv, and Terry Welch. It was published by Welch in 1984 as an improvement to the LZ78 algorithm published
Lempel–Ziv–Welch
Process in bioinformatics that identifies equivalent sites within molecular sequences
extremely numerous sequences that cannot be aligned solely by human effort. Various algorithms were devised to produce high-quality sequence alignments, and
Sequence_alignment
Technique in digital signal processing
Goertzel algorithm applies a single real-valued coefficient at each iteration, using real-valued arithmetic for real-valued input sequences. For covering
Goertzel_algorithm
Sequence of locally optimal choices
A greedy algorithm is an algorithm which, at each step, makes the choice that is locally optimal, and subsequently does not reconsider past choices. Greedy
Greedy_algorithm
Algorithm in mathematics
makes use of the forward-backward algorithm to compute the statistics for the expectation step. The Baum–Welch algorithm, the primary method for inference
Baum–Welch_algorithm
Algorithm that generates an approximation of a random number sequence
generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. The
Pseudorandom_number_generator
Monte Carlo algorithm
statistical physics, the Metropolis–Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability
Metropolis–Hastings_algorithm
Computer architecture hardware algorithm
Tomasulo's algorithm is a computer architecture hardware algorithm for dynamic scheduling of instructions that allows out-of-order execution and enables
Tomasulo's_algorithm
Greatest common divisor of polynomials
also the first step in most polynomial factorization algorithms. The Sturm sequence of a polynomial with real coefficients is the sequence of the remainders
Polynomial greatest common divisor
Polynomial_greatest_common_divisor
Turing-complete esoteric programming language invented by John Conway
only occurs if the exponent of 2, n + 1, is a prime. A step-by-step explanation of Conway's algorithm can be found in Havil (2007). For this program, reaching
FRACTRAN
Infinite sequence in mathematics
use this representation to reason about the sequence. The Kolakoski sequence may be generated by an algorithm that, in the i-th iteration, reads the value
Kolakoski_sequence
Available computing resource
Project scheduling method for repetitive activities Sequence step algorithm – Computer Algorithm System monitor – Component that monitors resources in
System_resource
Standard for the encryption of electronic data
Standard (DES), which had been published in 1977. The algorithm described by AES is a symmetric-key algorithm, meaning the same key is used for both encrypting
Advanced_Encryption_Standard
Project scheduling method for repetitive activities
project management topics Project management Project planning Sequence step algorithm Time distance diagram Work breakdown structure Kenley, Russell;
Linear_scheduling_method
Inference algorithm for hidden Markov models
forward–backward algorithm is an inference algorithm for hidden Markov models which computes the posterior marginals of all hidden state variables given a sequence of
Forward–backward_algorithm
Algorithm in numerical analysis
summation algorithm, also known as compensated summation, significantly reduces the numerical error in the total obtained by adding a sequence of finite-precision
Kahan_summation_algorithm
Algorithm to calculate eigenvalues
In numerical linear algebra, the QR algorithm or QR iteration is an eigenvalue algorithm: that is, a procedure to calculate the eigenvalues and eigenvectors
QR_algorithm
Class of algorithms in computational geometry
a convex sequence of vertices on the stack, the ones that have not yet been identified as being within pockets. At each step, the algorithm follows a
Convex_hull_algorithms
Optimization algorithm
people represent the algorithm, and the path taken down the mountain represents the sequence of parameter settings that the algorithm will explore. The steepness
Gradient_descent
Materials science algorithm
The rainflow-counting algorithm is used in calculating the fatigue life of a component in order to convert a loading sequence of varying stress into a
Rainflow-counting_algorithm
Problem in computer science
similarly fast algorithm for the all-pairs shortest paths problem. Maximum subarray problems arise in many fields, such as genomic sequence analysis and
Maximum_subarray_problem
Algorithmic problem on pairs of sequences
tested in time linear in the lengths of the remaining sequences, so the time for this algorithm would be O ( 2 n 1 ∑ i > 1 n i ) . {\displaystyle O\left(2^{n_{1}}\sum
Longest_common_subsequence
Bioinformatics search algorithm
search tool) is an algorithm and program for comparing primary biological sequence information, such as the amino-acid sequences of proteins, nucleotides
BLAST_(biotechnology)
Algorithm operating on grammar-like rules
applying the normal algorithm to an arbitrary string V {\displaystyle V} in the alphabet of this algorithm is a discrete sequence of elementary steps
Markov_algorithm
Ancient algorithm for generating prime numbers
equal this new number (which is the next prime), and repeat from step 3. When the algorithm terminates, the numbers remaining not marked in the list are all
Sieve_of_Eratosthenes
Algorithm in graph theory
degree sequence exists, or proves that one cannot find a positive answer. This construction is based on a recursive algorithm. The algorithm was published
Havel–Hakimi_algorithm
Binary arithmetic algorithm
programming, the exclusive or swap (sometimes shortened to XOR swap) is an algorithm that uses the exclusive or bitwise operation to swap the values of two
XOR_swap_algorithm
Method for finding sums of unit fractions
Leonardo of Pisa (Fibonacci). It is called a greedy algorithm because at each step the algorithm chooses greedily the largest possible unit fraction that
Greedy algorithm for Egyptian fractions
Greedy_algorithm_for_Egyptian_fractions
Optimization algorithm
computer science and operations research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems
Ant colony optimization algorithms
Ant_colony_optimization_algorithms
Algorithm for the travelling salesman problem
terminate. Else, go to step 3. The sequence of the visited vertices is the output of the algorithm. The nearest neighbour algorithm is easy to implement
Nearest_neighbour_algorithm
Program to compare computer programming languages
The TPK algorithm is a simple program introduced by Donald Knuth and Luis Trabb Pardo to illustrate the evolution of computer programming languages. In
TPK_algorithm
Discrete Fourier transform algorithm
Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT), or its inverse (IDFT), of a sequence. A Fourier transform converts
Fast_Fourier_transform
Algorithm used for pathfinding and graph traversal
heuristic. The algorithm described so far only gives the length of the shortest path. To find the actual sequence of steps, the algorithm can be easily
A*_search_algorithm
Algorithm for integer multiplication
The Karatsuba algorithm is a fast multiplication algorithm for integers. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. It is a
Karatsuba_algorithm
to create multiple sequence alignments of amino acid or nucleotide sequences. Published in 2002, the first version used an algorithm based on progressive
MAFFT
Algorithm for caching data
policies (also known as cache replacement algorithms or cache algorithms) are optimizing instructions or algorithms which a computer program or hardware-maintained
Cache_replacement_policies
Algorithm from machine learning
name winnow). It is a simple algorithm that scales well to high-dimensional data. During training, Winnow is shown a sequence of positive and negative examples
Winnow_(algorithm)
Algorithm that outputs all solutions to a problem
input x the algorithm produces the (possibly infinite) sequence y such that y has no duplicate and z∈y if and only if (x,z)∈R. The algorithm should halt
Enumeration_algorithm
String searching algorithm
persists across multiple searches. The Boyer–Moore algorithm uses information gathered during the preprocess step to skip sections of the text, resulting in a
Boyer–Moore string-search algorithm
Boyer–Moore_string-search_algorithm
Searching for patterns in text
This may significantly slow some search algorithms. One of many possible solutions is to search for the sequence of code units instead, but doing so may
String-searching_algorithm
Limited memory technique for decoding free codes
and algorithm. Metrics include: Fano metric Zigangirov metric Gallager metric Algorithms include: Stack algorithm Fano algorithm Creeper algorithm Given
Sequential_decoding
Combinatorial algorithm
permutations in the resulting sequence differ by swapping two adjacent permuted elements. Equivalently, this algorithm finds a Hamiltonian cycle in the
Steinhaus–Johnson–Trotter algorithm
Steinhaus–Johnson–Trotter_algorithm
Method of DNA sequence reconstruction
and nearly identical sequences (known as repeats) which can, in the worst case, increase the time and space complexity of algorithms quadratically; DNA
Sequence_assembly
Algorithm for measuring similarity between temporal sequences
analysis, dynamic time warping (DTW) is an algorithm for measuring similarity between two temporal sequences, which may vary in speed. For instance, similarities
Dynamic_time_warping
Sequence merge algorithm in computer science
In computer science, k-way merge algorithms or multiway merges are a specific type of sequence merge algorithms that specialize in taking in k sorted lists
K-way_merge_algorithm
Computer science algorithm
when the algorithm has backtracked past the original "root" vertex from the very first step. DFS is the basis for many graph-related algorithms, including
Graph_traversal
Family of iterative methods
the fact that the algorithm is very sensitive to the choice of the step size sequence, and the supposed asymptotically optimal step size policy can be
Stochastic_approximation
Method for division with remainder
A division algorithm is an algorithm which, given two integers N and D (respectively the numerator and the denominator), computes their quotient and/or
Division_algorithm
Mathematical sequence
iterative algorithm. Prüfer sequences were first used by Heinz Prüfer to prove Cayley's formula in 1918. One can generate a labeled tree's Prüfer sequence by
Prüfer_sequence
Method of computing optimal strategies for last-success problems
Hence no quicker algorithm can possibly exist for all sequences, so that the odds algorithm is, at the same time, optimal as an algorithm. Bruss 2000 devised
Odds_algorithm
Hidden Markov model algorithm
the Viterbi algorithm is required. It computes the most likely state sequence given the history of observations, that is, the state sequence that maximizes
Forward_algorithm
Divide and conquer sorting algorithm
merge-sort) is an efficient, general-purpose, comparison-based sorting algorithm. Most implementations of merge sort are stable, which means that the relative
Merge_sort
System used in computer graphics applications
A Block Matching Algorithm is a way of locating matching macroblocks in a sequence of digital video frames for the purposes of motion estimation. The
Block-matching_algorithm
Method of searching a sorted array
and q one position back in the Fibonacci sequence); then return to Step 2 [Increase i] If p=1, the algorithm terminates unsuccessfully. Otherwise set
Fibonacci_search_technique
Agglomerative hierarchical clustering method
linkage algorithm is composed of the following steps: Begin with the disjoint clustering having level L ( 0 ) = 0 {\displaystyle L(0)=0} and sequence number
Single-linkage_clustering
Fast greatest common divisor algorithm
algorithm is often used with integers represented using a base β such as β = 1000 or β = 232. Lehmer noted that most of the quotients from each step of
Lehmer's_GCD_algorithm
Method of machine learning
gradient descent algorithm. In this case, the complexity for n steps of this algorithm reduces to O(nd). The storage requirements at every step i are constant
Online_machine_learning
Algorithm that arranges lists in order
In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order. The most frequently used orders are numerical order
Sorting_algorithm
Cipher method
step (2) shift all letters in the counter-clockwise sequence beginning with zenith-2 ("E") down to and including the nadir ("O"), moving the sequence
Chaocipher
Data compression approach allowing perfect reconstruction of the original data
data. The primary encoding algorithms used to produce bit sequences are Huffman coding (also used by the deflate algorithm) and arithmetic coding. Arithmetic
Lossless_compression
Integer factorization algorithm
into a slow version of Pollard's algorithm. Choose some integer A greater than 2 which characterizes the Lucas sequence: V 0 = 2 , V 1 = A , V j = A V j
Williams's_p_+_1_algorithm
Vector quantization algorithm minimizing the sum of squared deviations
monotonically decreasing sequence. This guarantees that the k-means always converges, but not necessarily to the global optimum. The algorithm has converged when
K-means_clustering
Doubly exponential integer sequence
possible to interpret the Sylvester sequence as the result of a greedy algorithm for Egyptian fractions, that at each step chooses the smallest possible denominator
Sylvester's_sequence
Algorithm to transform a regular expression into a finite automaton
small informal one with the result, and a bigger with a step by step application of the algorithm. The picture below shows the result of Thompson's construction
Thompson's_construction
Numerical optimization algorithm
estimate at step k, and λ k {\displaystyle \lambda _{k}} is a parameter (called step size) which partly determines the particular algorithm. For the BHHH
Berndt–Hall–Hall–Hausman algorithm
Berndt–Hall–Hall–Hausman_algorithm
Algorithm used in data compression
a preparatory step to improve the efficiency of a compression algorithm, and is used this way in software such as bzip2. The algorithm can be implemented
Burrows–Wheeler_transform
Simple sorting algorithm using comparisons
Step by step bubble sort Reset Next step 44 3 7 1 Comparing A and ASwapping since > Continuing since ≯ The list is sorted 0 The bubble sort algorithm
Bubble_sort
Greatest integer less than or equal to square root
integers. Algorithms that compute (the decimal representation of) y run forever on each input y which is not a perfect square. Algorithms that compute
Integer_square_root
Mathematical version of an order change
ordering; Steinhaus–Johnson–Trotter algorithm; Heap's algorithm; Ehrlich's star-transposition algorithm: in each step, the first entry of the permutation
Permutation
Sequentially looking in an array
making the algorithm faster. The search will reach the sentinel if the target is not contained within the list. Set i to 0. If Li = T, go to step 4. Increase
Linear_search
Algorithm for supervised learning of binary classifiers
In machine learning, the perceptron is an algorithm for supervised learning of binary classifiers. A binary classifier is a function that can decide whether
Perceptron
Alignment of more than two molecular sequences
global optimum for n sequences this way has been shown to be an NP-complete problem. In 1989, based on Carrillo-Lipman Algorithm, Altschul introduced
Multiple_sequence_alignment
Statistical Markov model
difficult: for a sequence of length T, a straightforward Viterbi algorithm has complexity O(N2KT). To find an exact solution, a junction tree algorithm could be
Hidden_Markov_model
Type of stable matching problem
obtained by a sequence of rotation eliminations on the stable table. These rotation eliminations comprise Phase 2 of Irving's algorithm. By 2, if each
Stable_roommates_problem
Algorithm that multiplies two signed binary numbers in two's complement notation
multiplication algorithm is a multiplication algorithm that multiplies two signed binary numbers in two's complement notation. The algorithm was invented
Booth's multiplication algorithm
Booth's_multiplication_algorithm
Method in speedcubing
speedcubers memorize hundreds of algorithms for this step, including multiple algorithms for the same case. Alternatively, the F2L step can be solved using intuitive
CFOP_method
Algorithm for training neural networks
Teacher forcing is an algorithm for training the weights of recurrent neural networks (RNNs). It involves feeding observed sequence values (i.e. ground-truth
Teacher_forcing
Metaheuristic proposed by Xin-She Yang
firefly algorithm is a metaheuristic proposed by Xin-She Yang and inspired by the flashing behavior of fireflies. In pseudocode the algorithm can be stated
Firefly_algorithm
Mathematical folklore
{\displaystyle V} , then no algorithm performs better than blind search. Here, blind search means that at each step of the algorithm, the element v ∈ V {\displaystyle
No_free_lunch_theorem
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SEQUENCE STEP-ALGORITHM
SEQUENCE STEP-ALGORITHM
SEQUENCE STEP-ALGORITHM
SEQUENCE STEP-ALGORITHM
SEQUENCE STEP-ALGORITHM
SEQUENCE STEP-ALGORITHM
SEQUENCE STEP-ALGORITHM
SEQUENCE STEP-ALGORITHM
SEQUENCE STEP-ALGORITHM
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