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Optimization theory in computing
The approximate counting algorithm allows the counting of a large number of events using a small amount of memory. Invented in 1977 by Robert Morris of
Approximate counting algorithm
Approximate_counting_algorithm
Approximate distinct counting algorithm
HyperLogLog is an algorithm for the count-distinct problem, approximating the number of distinct elements in a multiset. Calculating the exact cardinality
HyperLogLog
Sorting algorithm
integer sorting algorithm. It operates by counting the number of objects that possess distinct key values, and applying prefix sum on those counts to determine
Counting_sort
Algorithm that employs a degree of randomness as part of its logic or procedure
functions. Approximate counting algorithm Atlantic City algorithm Bogosort Count–min sketch HyperLogLog Karger's algorithm Las Vegas algorithm Monte Carlo
Randomized_algorithm
simulations Algorithms for calculating variance: avoiding instability and numerical overflow Approximate counting algorithm: allows counting large number
List_of_algorithms
Finding strings that approximately match a pattern
algorithms. Oxford [Oxfordshire]: Oxford University Press. ISBN 978-0-19-511367-9. Myers, G. (May 1999). "A fast bit-vector algorithm for approximate
Approximate_string_matching
Algorithm that arranges lists in order
4427n+O(\log {n})} comparisons. Algorithms not based on comparisons, such as counting sort, can have better performance. Sorting algorithms are prevalent in introductory
Sorting_algorithm
Quantum algorithm for counting solutions to search problems
Quantum counting algorithm is a quantum algorithm for efficiently counting the number of solutions for a given search problem. The algorithm is based
Quantum_counting_algorithm
Class of algorithms operating on data streams
constraints, streaming algorithms often produce approximate answers based on a summary or "sketch" of the data stream. Though streaming algorithms had already been
Streaming_algorithm
Optimization algorithms using quantum computing
quantum approximate optimization algorithm (QAOA) briefly had a better approximation ratio than any known polynomial time classical algorithm (for a certain
Quantum optimization algorithms
Quantum_optimization_algorithms
Algorithm to be run on quantum computers
In quantum computing, a quantum algorithm is an algorithm that runs on a realistic model of quantum computation, the most commonly used model being the
Quantum_algorithm
The lossy count algorithm is an algorithm to identify elements in a data stream whose frequency exceeds a user-given threshold. The algorithm works by
Lossy_Count_Algorithm
Quantum algorithm for eigenvalue estimation
quantum algorithms, such as Shor's algorithm, the quantum algorithm for linear systems of equations, and the quantum counting algorithm. The algorithm operates
Quantum phase estimation algorithm
Quantum_phase_estimation_algorithm
Sequence of operations for a task
restrictions anyway. In the general case, a specialized algorithm or an algorithm that finds approximate solutions is used, depending on the difficulty of the
Algorithm
Estimate of time taken for running an algorithm
takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that
Time_complexity
chances of a probabilistic algorithm to succeed. Apparently first used in 1986 by Jerrum et al. for approximate counting algorithms, the technique was later
Median_trick
Data structure for approximate set membership
filters can be used for approximate data synchronization as in Byers et al. (2004). Counting Bloom filters can be used to approximate the number of differences
Bloom_filter
Efficient algorithm to count points on elliptic curves
Schoof's algorithm is an efficient algorithm to count points on elliptic curves over finite fields. The algorithm has applications in elliptic curve cryptography
Schoof's_algorithm
Search algorithm used in sorted arrays
half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position of a target value within a sorted array. Binary
Binary_search
Algorithm for estimating a count of distinct elements
(the count-distinct problem). The algorithm was introduced by Philippe Flajolet and G. Nigel Martin in their 1984 article "Probabilistic Counting Algorithms
Flajolet–Martin_algorithm
Complexity class
has a polynomial-time Turing reduction or polynomial-time counting reduction to it. A counting reduction is a pair of polynomial-time transformations from
♯P-complete
Discrete Fourier transform algorithm
FFT. Another algorithm for approximate computation of a subset of the DFT outputs is due to Shentov et al. (1995). The Edelman algorithm works equally
Fast_Fourier_transform
Algorithms for zeros of functions
In numerical analysis, a root-finding algorithm is an algorithm for finding zeros, also called roots, of a function. A root of the function f is a number
Root-finding_algorithm
Algorithm used by Google Search to rank web pages
PageRank (PR) is an algorithm used by Google Search to rank web pages in their search engine results. It is named after both the term "web page" and co-founder
PageRank
Fractal analysis technique
box counting is to move the box according to some feature related to the pixels of interest. In local connected dimension box counting algorithms, for
Box_counting
Quantum algorithm for integer factorization
Shor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor
Shor's_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
Computer science metric of string similarity
without allowing edit operations). A similar algorithm for approximate string matching is the bitap algorithm, also defined in terms of edit distance. Levenshtein
Edit_distance
Unrelated vertices in graphs
there is an efficient algorithm for solving it. The maximum independent set problem is NP-hard and it is also hard to approximate. Despite the close relationship
Independent set (graph theory)
Independent_set_(graph_theory)
Algorithms to complete a sudoku
first row, would work in opposition to the algorithm. Thus the program would spend significant time "counting" upward before it arrives at the grid which
Sudoku_solving_algorithms
Problem of finding the longest simple path for a given graph
Stronger hardness results are also known showing that it is difficult to approximate. However, it has a linear time solution for directed acyclic graphs,
Longest_path_problem
Method of a dimension reduction
Count sketch is a type of dimensionality reduction that is particularly efficient in statistics, machine learning and algorithms. It was invented by Moses
Count_sketch
Searching for patterns in text
A string-searching algorithm, sometimes called string-matching algorithm, is an algorithm that searches a body of text for portions that match by pattern
String-searching_algorithm
Algorithm for finding the shortest paths in graphs
better ones until they eventually reach the solution. In both algorithms, the approximate distance to each vertex is always an overestimate of the true
Bellman–Ford_algorithm
Algorithm for solving a puzzle or game in the fewest possible moves
God's algorithm of the Rubik cube is a notion originating in discussions of ways to solve the Rubik's Cube puzzle, but which can also be applied to other
God's_algorithm
Concept in statistics
(under a different name) by Aviad Cohen and Itamar Procaccia, as an approximate algorithm to compute an exact regularity statistic, Kolmogorov–Sinai entropy
Approximate_entropy
Determines the points needed for rasterizing a circle
circle algorithm is an algorithm used to determine the points needed for rasterizing a circle. It is a generalization of Bresenham's line algorithm. The
Midpoint_circle_algorithm
Competitive algorithm for searching a problem space
genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA) in
Genetic_algorithm
Monte Carlo algorithm
known in statistical mechanics as the heat bath algorithm, is a Markov chain Monte Carlo (MCMC) algorithm for sampling from a specified multivariate probability
Gibbs_sampling
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
gives the approximate volume of the original body. This work earned its authors the 1991 Fulkerson Prize. Although the time for this algorithm is polynomial
Convex_volume_approximation
Function representing the number of primes less than or equal to a given number
written as ln(x) or loge(x). In mathematics, the prime-counting function is the function counting the number of prime numbers less than or equal to some
Prime-counting_function
Algorithms and methods of plotting the Mandelbrot set on a computing device
the iter count non-linearly and scales the palette to cycle approximately proportionally to the zoom. We can then plug v into whatever algorithm we desire
Plotting algorithms for the Mandelbrot set
Plotting_algorithms_for_the_Mandelbrot_set
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
Algorithms which recursively solve subproblems
originally a political maxim, designates an algorithm design paradigm. A divide-and-conquer algorithm recursively breaks down a problem into two or
Divide-and-conquer_algorithm
Problem in combinatorial optimization
computationally complex algorithms, there has been substantial research on creating and analyzing algorithms that approximate a solution. The knapsack
Knapsack_problem
Annual conference series on algorithms
The European Symposium on Algorithms (ESA) is an international conference covering the field of algorithms. It has been held annually since 1993, typically
European Symposium on Algorithms
European_Symposium_on_Algorithms
Experimental technology level
quantum approximate optimization algorithm (QAOA), which use NISQ devices but offload some calculations to classical processors. These algorithms have been
Noisy intermediate-scale quantum computing
Noisy_intermediate-scale_quantum_computing
Iterative method for finding maximum likelihood estimates in statistical models
variational view of the EM algorithm, as described in Chapter 33.7 of version 7.2 (fourth edition). Variational Algorithms for Approximate Bayesian Inference
Expectation–maximization algorithm
Expectation–maximization_algorithm
List of quantum computing algorithms
algorithms, including algorithms, algorithmic techniques, computational models, and problem frameworks used in quantum computing. A quantum algorithm
List_of_quantum_algorithms
Sorting algorithm
the range of possible key values are approximately the same. It requires O(n + N) time. It is similar to counting sort, but differs in that it "moves items
Pigeonhole_sort
Problem of constructing equal-area shapes
impossible if π were transcendental, but that fact was not proven until 1882. Approximate constructions with any given non-perfect accuracy exist, and many such
Squaring_the_circle
comparison of algorithms. Thistlethwaite's four-phase algorithm is not designed to search for an optimal solution, its average move count being about 31
Optimal solutions for the Rubik's Cube
Optimal_solutions_for_the_Rubik's_Cube
Sorting algorithm
Bucket sort, or bin sort, is a sorting algorithm that works by distributing the elements of an array into a number of buckets. Each bucket is then sorted
Bucket_sort
Method for finding kth smallest value
In computer science, a selection algorithm is an algorithm for finding the k {\displaystyle k} th smallest value in a collection of orderable values,
Selection_algorithm
British computer scientist
Currently, he focuses on the complexity of counting and the efficiency of Markov chain algorithms for approximate counting. Four key contributions made by Martin
Martin_Dyer
Simple routing algorithm sending incoming packets to all links other than the sender
Flooding is used in computer network routing algorithms in which every incoming packet is sent through every outgoing link except the one it arrived on
Flooding (computer networking)
Flooding_(computer_networking)
Process of reducing words to word stems
based on counting the over-stemming and under-stemming errors. Unsolved problem in computer science Is there any perfect stemming algorithm in English
Stemming
Multidimensional search tree for points in k dimensional space
of k-d tree based nearest neighbor and approximate nearest neighbor algorithms CGAL the Computational Algorithms Library, has an implementations of k-d
K-d_tree
Inverse function to a tower of powers
randomized O(n log* n) time. Fürer's algorithm for integer multiplication: O(n log n 2O(lg* n)). Finding an approximate maximum (element at least as large
Iterated_logarithm
Decision problem in computer science
exactly. Then, the polynomial time algorithm for approximate subset sum becomes an exact algorithm with running time polynomial in n and 2 P {\displaystyle
Subset_sum_problem
Numerical eigenvalue calculation
The Lanczos algorithm is an iterative method devised by Cornelius Lanczos that is an adaptation of power methods to find the m {\displaystyle m} "most
Lanczos_algorithm
Number, approximately 3.14
Archimedes created an algorithm to approximate π with arbitrary accuracy. In the 5th century AD, Chinese mathematicians approximated π to seven digits, while
Pi
Study of resources used by an algorithm
computer science, the analysis of algorithms is the process of finding the computational complexity of algorithms—the amount of time, storage, or other
Analysis_of_algorithms
Task of computing complete subgraphs
P ≠ NP) it is not even possible to approximate the problem accurately and efficiently. Clique-finding algorithms have been used in chemistry, to find
Clique_problem
Calculating method used in ancient China
mechanical method of algorithmic computation with counting rods in China from the Warring States to Ming dynasty before the counting rods were increasingly
Rod_calculus
Quantum algorithm for solving systems of linear equations
The Harrow–Hassidim–Lloyd (HHL) algorithm is a quantum algorithm for obtaining certain limited information about the solution to a system of linear equations
HHL_algorithm
Algorithms for calculating square roots
max plus beta min algorithm nth root algorithm Fast inverse square root The factors two and six are used because they approximate the geometric means
Square_root_algorithms
Indian American professor of computer science (born 1957)
equivalence between random generation and approximate counting. During the 1990s he worked mostly on approximation algorithms, championing the primal-dual schema
Vijay_Vazirani
Logic problem, AND of pairwise ORs
Kasiviswanathan, Shiva Prasad (2007), "Algorithms for counting 2-SAT solutions and colorings with applications", Algorithmic Aspects in Information and Management
2-satisfiability
Sequence in computer science
of computation, prefix sums are a useful primitive in certain algorithms such as counting sort, and they form the basis of the scan higher-order function
Prefix_sum
Economical computational problem
performance of their algorithm. Lipton, Markakis and Mehta presented a Quasi-polynomial time algorithm for computing an approximate NE. It takes time n
Nash_equilibrium_computation
Computational task of sorting whole numbers
sorting algorithms including pigeonhole sort, counting sort, and radix sort are widely used and practical. Other integer sorting algorithms with smaller
Integer_sorting
Methodic assignment of colors to elements of a graph
21 NP-complete problems from 1972, and at approximately the same time various exponential-time algorithms were developed based on backtracking and on
Graph_coloring
Scientific prize and lecture series
the topic of approximate counting repeatedly during his career, starting with the Flajolet–Martin algorithm for probabilistic counting and leading the
Flajolet_Lecture_Prize
by the samples.[BCE] In two dimensions, a more accurate approximation algorithm is known, for which the approximation error is a small multiple of the
Simplicial_depth
Algorithm in mathematics
computing and bioinformatics, the Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the unknown parameters of a
Baum–Welch_algorithm
Computational problem in graph theory
blocking flow algorithm of Goldberg and Rao. The algorithms of Sherman and Kelner, Lee, Orecchia and Sidford, respectively, find an approximately optimal maximum
Maximum_flow_problem
Type of finite-state machine in automata theory
an algorithm for compiling a regular expression to an NFA that can efficiently perform pattern matching on strings. Conversely, Kleene's algorithm can
Nondeterministic finite automaton
Nondeterministic_finite_automaton
NP-hard problem in combinatorial optimization
Rosenkrantz, D. J.; Stearns, R. E.; Lewis, P. M. (14–16 October 1974). Approximate algorithms for the traveling salesperson problem. 15th Annual Symposium on
Travelling_salesman_problem
American computer scientist
Oxford. Her research concerns the design and analysis of algorithms for random sampling and approximate combinatorial enumeration. Goldberg did her undergraduate
Leslie_Ann_Goldberg
Randomized algorithm for minimum cuts
In computer science and graph theory, Karger's algorithm is a randomized algorithm to compute a minimum cut of a connected graph. It was invented by David
Karger's_algorithm
Search algorithm
A rapidly exploring random tree (RRT) is an algorithm designed to efficiently search nonconvex, high-dimensional spaces by randomly building a space-filling
Rapidly_exploring_random_tree
Grouping a set of objects by similarity
only for approximate solutions. A particularly well-known approximate method is Lloyd's algorithm, often just referred to as "k-means algorithm" (although
Cluster_analysis
Method for discovering interesting relations between variables in databases
Nobel, Andrew; Prins, Jan (2006). "Mining Approximate Frequent Itemsets in the Presence of Noise: Algorithm and Analysis". Proceedings of the 2006 SIAM
Association_rule_learning
Computer science award
hdl:10338.dmlcz/120489, S2CID 10838178 Sinclair, A.; Jerrum, M. (1989), "Approximate counting, uniform generation and rapidly mixing Markov chains", Information
Gödel_Prize
Numerical technique
Carlo method that numerically computes a definite integral. While other algorithms usually evaluate the integrand at a regular grid, Monte Carlo randomly
Monte_Carlo_integration
data structure used to test whether an element is a member of a set (an approximate membership query filter, AMQ). A query will elicit a reply specifying
Quotient_filter
Algorithmic technique
method is an algorithmic technique most commonly used for decision making and prediction, and also widely deployed in game theory and algorithm design. The
Multiplicative weight update method
Multiplicative_weight_update_method
Data compression approach allowing perfect reconstruction of the original data
compression algorithm can shrink the size of all possible data: Some data will get longer by at least one symbol or bit. Compression algorithms are usually
Lossless_compression
Method of executing orders
Algorithmic trading is a method of executing orders using automated pre-programmed trading instructions accounting for variables such as time, price,
Algorithmic_trading
Framework for mathematical analysis of machine learning
In computational learning theory, probably approximately correct (PAC) learning is a framework for mathematical analysis of machine learning. It was proposed
Probably approximately correct learning
Probably_approximately_correct_learning
Principle in artificial intelligence
learning has continued this trend. Computer vision. Algorithms that were assumed to approximate the human visual system (such as explicitly encoded edge
Bitter_lesson
Fractal geometry concept
an approximate value for the box-counting dimension of the graph of a real-valued function or time series. This value is obtained via an algorithmic approximation
Higuchi_dimension
Problem of counting solutions to logic formulas
Satisfiability Problem (sometimes called Sharp-SAT, #SAT or model counting) is the problem of counting the number of interpretations that satisfy a given Boolean
♯SAT
Algorithmic runtime requirements for matrix multiplication
Unsolved problem in computer science What is the fastest algorithm for matrix multiplication? More unsolved problems in computer science In theoretical
Computational complexity of matrix multiplication
Computational_complexity_of_matrix_multiplication
Mathematics award
computational complexity theory, logic of programming languages, analysis of algorithms, cryptography, computer vision, pattern recognition, information processing
IMU_Abacus_Medal
Attempts to formalize the concept of algorithms
Algorithm characterizations are attempts to formalize the word algorithm. Algorithm does not have a generally accepted formal definition. Researchers
Algorithm_characterizations
Field of machine learning
learning and optimal control, reinforcement learning (RL) (also known as approximate dynamic programming) is concerned with how an intelligent agent should
Reinforcement_learning
Alternative form of government or social ordering
also referred to as algorithmic regulation, regulation by algorithms, algorithmic governance, algocratic governance, algorithmic legal order, or algocracy
Government_by_algorithm
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APPROXIMATE COUNTING-ALGORITHM
APPROXIMATE COUNTING-ALGORITHM
APPROXIMATE COUNTING-ALGORITHM
APPROXIMATE COUNTING-ALGORITHM
APPROXIMATE COUNTING-ALGORITHM
APPROXIMATE COUNTING-ALGORITHM
APPROXIMATE COUNTING-ALGORITHM
APPROXIMATE COUNTING-ALGORITHM
APPROXIMATE COUNTING-ALGORITHM
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