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Algorithm that employs a degree of randomness as part of its logic or procedure
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random
Randomized_algorithm
Type of randomized algorithm
Carlo algorithm is a randomized algorithm whose output may be incorrect with a certain (typically small) probability. Two examples of such algorithms are
Monte_Carlo_algorithm
Problem in computer science
randomized ski-rental coin flipping algorithm is 1.8. The best randomized algorithm against an oblivious adversary is to choose some day i at random according
Ski_rental_problem
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
Sequence of operations for a task
each step, eventually producing output and terminating. Randomized algorithms incorporate random inputs which can be used to simulate non-deterministic
Algorithm
Random search tree data structure
In computer science, the treap and the randomized binary search tree are two closely related forms of binary search tree data structures that maintain
Treap
Binary sequence
Intuitively, an algorithmically random sequence (or random sequence) is a sequence of binary digits that appears random to any algorithm running on a (prefix-free
Algorithmically random sequence
Algorithmically_random_sequence
Type of randomized algorithm
In computing, a Las Vegas algorithm is a randomized algorithm that always gives correct results; that is, it always produces the correct result or it
Las_Vegas_algorithm
Sorting algorithm
k} is astronomically large. The following is a description of the randomized algorithm in pseudocode: function bogoSort(deck: List): while deck is not sorted:
Bogosort
Algorithm that arranges lists in order
big O notation, divide-and-conquer algorithms, data structures such as heaps and binary trees, randomized algorithms, best, worst and average case analysis
Sorting_algorithm
Algorithm whose behavior and output may depend on the run
science. In 1917, Henry C. Pocklington introduced a randomized algorithm known as Pocklington's algorithm for efficiently finding square roots modulo prime
Nondeterministic_algorithm
Type of computer science algorithm
simple randomized in-place algorithms for primality testing such as the Miller–Rabin primality test, and there are also simple in-place randomized factoring
In-place_algorithm
Algorithm for shuffling a finite sequence
element in the shuffled sequence by randomly drawing an element from the list until no elements remain. The algorithm produces an unbiased permutation:
Fisher–Yates_shuffle
Randomized algorithm
Reservoir sampling is a family of randomized online algorithms for choosing a simple random sample, without replacement, of k items from a population
Reservoir_sampling
Search algorithm
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
Combinatorial game theory concept to represent all possible game states
a deterministic algorithm, such as backward induction or retrograde analysis can be used. Randomized algorithms and minmax algorithms such as MCTS can
Game_tree
Overview of and topical guide to algorithms
eliminate candidate solutions Randomized algorithm — algorithm using randomness as part of its logic Approximation algorithm — algorithm that finds near-optimal
Outline_of_algorithms
Coding theory algorithm
decoding algorithm. The first two will be randomized algorithms while the last one will be a deterministic algorithm. Hamming distance : Given two vectors
Generalized minimum-distance decoding
Generalized_minimum-distance_decoding
Equivalence of average-case and expected complexity
the performance of randomized algorithms to deterministic (non-random) algorithms. It states that, for certain classes of algorithms, and certain measures
Yao's_principle
Type of matrix factorization
to an LU decomposition using a randomized algorithm. Given an input matrix A and a desired low rank k, the randomized LU returns permutation matrices
LU_decomposition
Computational problem of interest in computer science
+ 1 points). In 2011, a randomized algorithm with competitive bound Õ(log2k log3n) was found. In 2017, a randomized algorithm with competitive bound O(log6
K-server_problem
The randomized weighted majority algorithm is an algorithm in machine learning theory for aggregating expert predictions to a series of decision problems
Randomized weighted majority algorithm
Randomized_weighted_majority_algorithm
Randomized algorithm for verifying matrix multiplication
Freivalds' algorithm (named after Rūsiņš Mārtiņš Freivalds) is a probabilistic randomized algorithm used to verify matrix multiplication. Given three n × n
Freivalds'_algorithm
Tree-based ensemble machine learning methods
method of random decision forests was first proposed by Salzberg and Heath in 1993, with a method that used a randomized decision tree algorithm to create
Random_forest
Method for analyzing online algorithms
algorithms are analysed for average-case and worst-case data. Competitive analysis is a way of doing worst case analysis for on-line and randomized algorithms
Competitive analysis (online algorithm)
Competitive_analysis_(online_algorithm)
Automated methods for the creation of mazes
initially randomized or if a wall is randomly chosen from a nonrandom list, either way is just as easy to code. Because the effect of this algorithm is to
Maze_generation_algorithm
and randomized algorithms in a simpler and more efficient fashion than with deterministic algorithms. Unfortunately, this makes even simple randomized algorithms
Algorithm_engineering
Algorithm to search the nodes of a graph
science, depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting
Depth-first_search
generator Quantum algorithm Random-restart hill climbing Randomized algorithm Running time Sorting algorithm Search algorithm Stable algorithm (disambiguation)
List of algorithm general topics
List_of_algorithm_general_topics
Classification of algorithm
A galactic algorithm is an algorithm with record-breaking theoretical (asymptotic) performance, but which is not used due to practical constraints. Typical
Galactic_algorithm
Creating sequence of numbers that cannot be predicted
Random variable, contains a chance-dependent value Randomized algorithm Lugrin, Thomas (2023), "Random Number Generator", in Mulder, Valentin; Mermoud,
Random_number_generation
The expected linear time MST algorithm is a randomized algorithm for computing the minimum spanning forest of a weighted graph with no isolated vertices
Expected linear time MST algorithm
Expected_linear_time_MST_algorithm
Coppersmith–Winograd algorithm: square matrix multiplication Freivalds' algorithm: a randomized algorithm used to verify matrix multiplication Strassen algorithm: faster
List_of_algorithms
Sequence where any order is equally likely
variable of a set of objects. The use of random permutations is common in games of chance and in randomized algorithms in coding theory, cryptography, and
Random_permutation
Algorithmic technique
was in an algorithm named "fictitious play" which was proposed in game theory in the early 1950s. Grigoriadis and Khachiyan applied a randomized variant
Multiplicative weight update method
Multiplicative_weight_update_method
Type of randomized algorithm
In computing, an Atlantic City algorithm is a randomized algorithm that answers correctly at least 75% of the time. In some variant definitions, the correctness
Atlantic_City_algorithm
Apparent lack of pattern or predictability in events
introduction of randomness into computations can be an effective tool for designing better algorithms. In some cases, such randomized algorithms even outperform
Randomness
Partition of a simple polygon into triangles
triangulated in linear time, though the proposed algorithm is very complex. A simpler randomized algorithm with linear expected time is also known. The time
Polygon_triangulation
Divide and conquer sorting algorithm
merge sort and heapsort for randomized data, particularly on larger distributions. Quicksort is a divide-and-conquer algorithm. It works by selecting a "pivot"
Quicksort
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
Type of algorithm in computer science
reference value may represent an unsuccessful (out-of-domain) result. Randomized algorithm Lee, Edward A. "The Problem with Threads" (PDF). Retrieved 2009-05-29
Deterministic_algorithm
Approximate distinct counting algorithm
The basis of the HyperLogLog algorithm is the observation that the cardinality of a multiset of uniformly distributed random numbers can be estimated by
HyperLogLog
equal elements; it may also be solved in linear expected time by a randomized algorithm that inserts each item into a hash table and compares only those
Element_distinctness_problem
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
Sweep line algorithm
In computational geometry, the Bentley–Ottmann algorithm is a sweep line algorithm for listing all crossings in a set of line segments, i.e. it finds
Bentley–Ottmann_algorithm
Tool for working with matrices
application is for the problem of fair random assignment: given a randomized allocation of items, Birkhoff's algorithm can decompose it into a lottery on
Birkhoff_algorithm
Computational geometry problem
systematic study of the computational complexity of geometric algorithms. Randomized algorithms that solve the problem in linear time are known, in Euclidean
Closest pair of points problem
Closest_pair_of_points_problem
Topic in computer science
testing algorithm. Formally, a property testing algorithm with query complexity q(n) and proximity parameter ε for a decision problem L is a randomized algorithm
Property_testing
Theorem in computational complexity theory
checked by a randomized algorithm) of constant query complexity and logarithmic randomness complexity (uses a logarithmic number of random bits). The PCP
PCP_theorem
Randomized polynomial time class of computational complexity theory
characterization makes the fact that RP is a subset of NP obvious. Randomized algorithm This comparison is attributed to Michael O. Rabin on p. 252 of Gasarch
RP_(complexity)
Estimate of time taken for running an algorithm
includes algorithms with the time complexities defined above. The specific term sublinear time algorithm commonly refers to randomized algorithms that sample
Time_complexity
and operations research, randomized rounding is a widely used approach for designing and analyzing approximation algorithms. Many combinatorial optimization
Randomized_rounding
Independent set which is not a subset of any other independent set
In order to show that their algorithm is in N C 2 {\displaystyle NC_{2}} , they initially presented a randomized algorithm that uses O ( m ) {\displaystyle
Maximal_independent_set
Random self-reducibility (RSR) is the rule that a good algorithm for the average case implies a good algorithm for the worst case. RSR is the ability to
Random_self-reducibility
Automated method for solving mazes
maze-solving algorithm is an automated method for solving a maze. The random mouse, wall follower, Pledge, Tarry's, and Trémaux's algorithms are designed
Maze-solving_algorithm
Unsolved problem on graph query complexity
{\displaystyle n} vertices. Versions of the problem for randomized algorithms and quantum algorithms have also been formulated and studied. The deterministic
Aanderaa–Karp–Rosenberg conjecture
Aanderaa–Karp–Rosenberg_conjecture
Method for finding minimum spanning trees
combining Prim's algorithm with Borůvka's. A faster randomized minimum spanning tree algorithm based in part on Borůvka's algorithm due to Karger, Klein
Borůvka's_algorithm
7/4-competitive. There are other randomized algorithms that perform better than BIT. In 1995, a randomized algorithm with competitive ratio of 1.6 was
List_update_problem
Subfield of information theory and computer science
and the relations between them: algorithmic complexity, algorithmic randomness, and algorithmic probability. Algorithmic information theory principally
Algorithmic information theory
Algorithmic_information_theory
Method in which data is created algorithmically as opposed to manually
type of formal grammar Linear congruential generator – Algorithm for generating pseudo-randomized numbers List of games using procedural generation Noise
Procedural_generation
Algorithm that generates an approximation of a random number sequence
random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers
Pseudorandom_number_generator
Deterministic quantum algorithm
and the first two output values are different. For a conventional randomized algorithm, a constant k {\displaystyle k} evaluations of the function suffices
Deutsch–Jozsa_algorithm
Algorithm characteristic in computations
input to an algorithm, which leads to the problem of devising a probability distribution over inputs. Alternatively, a randomized algorithm can be used
Average-case_complexity
Computer hardware technology that uses quantum mechanics
While programmers may depend on probability theory when designing a randomized algorithm, quantum-mechanical notions such as superposition and wave interference
Quantum_computing
randomized algorithm with numeric output multiple times, and use the median of the obtained results as a final answer. For example, if an algorithm takes
Median_trick
Least-weight tree connecting graph vertices
linear time randomized algorithm based on a combination of Borůvka's algorithm and the reverse-delete algorithm. The fastest non-randomized comparison-based
Minimum_spanning_tree
Problem in combinatorial optimization
meet-in-the-middle algorithm, using insights from Schroeppel and Shamir's Algorithm for Subset Sum, provides as a corollary a randomized algorithm for Knapsack
Knapsack_problem
Set of edges without common vertices
greedy algorithm is 1/2-competitive. For the unweighted maximization case with a random arrival model, Karp, Vazirani and Vazirani gave a randomized algorithm
Matching_(graph_theory)
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
On constructing objects that obey a system of constraints with limited dependence
independent random variables P {\displaystyle {\mathcal {P}}} in Ω, Robin Moser and Gábor Tardos proposed an efficient randomized algorithm that computes
Algorithmic Lovász local lemma
Algorithmic_Lovász_local_lemma
Class of functions in cryptography
(UP) Fk is a permutation whose values cannot be predicted by a fast randomized algorithm. Unpredictable permutations may be used as a cryptographic primitive
Pseudorandom_permutation
technique used in analysis of randomized algorithms. A randomized algorithm makes a set of random choices. These random choices may be intricately related
Principle of deferred decision
Principle_of_deferred_decision
Israeli mathematician and computer scientist (1931–2026)
While there, Rabin invented the Miller–Rabin primality test, a randomized algorithm that can determine very quickly (but with a tiny probability of error)
Michael_O._Rabin
Computer science algorithm
1. An analogous competitive lower bound of Ω(n) also holds for randomized algorithms that know the coordinates of each node in a geometric embedding
Graph_traversal
Computer program for the Boolean satisfiability problem
complete algorithms, such as DPLL. In contrast, randomized algorithms like the PPSZ algorithm by Paturi, Pudlak, Saks, and Zane set variables in a random order
SAT_solver
Collection of random variables
particularly in the analysis and development of randomized algorithms. These algorithms utilize random inputs to simplify problem-solving or enhance performance
Stochastic_process
Concept in computer science
A Monte Carlo algorithm is a randomized algorithm which is likely to be correct. Problems in the class BPP have Monte Carlo algorithms with polynomial
BPP_(complexity)
Concept in computer science
randomization does not help against it. From S. Ben-David, A. Borodin, R. Karp, G. Tardos, A. Wigderson we have: If there is a randomized algorithm that
Adversary_model
American computer scientist
Google. His research spans algorithms, web search and databases. He is the co-author of the textbooks Randomized Algorithms with Rajeev Motwani and Introduction
Prabhakar_Raghavan
Proof checkable by a randomized algorithm
checked by a randomized algorithm using a bounded amount of randomness and reading a bounded number of bits of the proof. The algorithm is then required
Probabilistically checkable proof
Probabilistically_checkable_proof
Technique for selecting hash functions
computing, universal hashing (in a randomized algorithm or data structure) refers to selecting a hash function at random from a family of hash functions
Universal_hashing
Mapping arbitrary data to fixed-size values
representation of the board position. A universal hashing scheme is a randomized algorithm that selects a hash function h among a family of such functions,
Hash_function
approximate solution can be found with the following very simple randomized algorithm: Send each subject to the treatment group with probability 1/2. In
Set_balancing
For generation of random factorized numbers
Bach's algorithm is a probabilistic polynomial time algorithm for generating random numbers along with their factorization. It was published by Eric Bach
Bach's_algorithm
Sampling technique
distribution. Several efficient algorithms for simple random sampling have been developed. A naive algorithm is the draw-by-draw algorithm where at each step we
Simple_random_sample
literals, the simple randomized approximation algorithm which assigns a truth value to each variable independently and uniformly at random satisfies 7/8 of
Karloff–Zwick_algorithm
Type of approximation algorithm
may admit a randomized algorithm with similar properties, a polynomial-time randomized approximation scheme or PRAS. A PRAS is an algorithm which takes
Polynomial-time approximation scheme
Polynomial-time_approximation_scheme
Optimization algorithm
technique which belongs to the family of local search. It is an iterative algorithm that starts with an arbitrary solution to a problem, then attempts to
Hill_climbing
Algorithm
Kaczmarz algorithm as a special case. Other special cases include randomized coordinate descent, randomized Gaussian descent and randomized Newton method
Kaczmarz_method
Probabilistic data structure in computer science
benefit. Conservative updating changes the update, but not the query algorithms. To count c instances of event type i, one first computes an estimate
Count–min_sketch
Monte Carlo algorithm
inference. It is a randomized algorithm (i.e. an algorithm that makes use of random numbers), and is an alternative to deterministic algorithms for statistical
Gibbs_sampling
Image segmentation algorithm
The random walker algorithm is an algorithm for image segmentation. In the first description of the algorithm, a user interactively labels a small number
Random_walker_algorithm
Statistical method for fitting a line
Dillencourt, Michael B.; Mount, David M.; Netanyahu, Nathan S. (1992), "A randomized algorithm for slope selection", International Journal of Computational Geometry
Theil–Sen_estimator
Probabilistic problem-solving algorithm
Monte Carlo simulations, are a broad class of computational algorithms based on repeated random sampling for obtaining numerical results, conceptualized
Monte_Carlo_method
Method for numerical integration
The nested sampling algorithm is a computational approach to the Bayesian statistics problems of comparing models and generating samples from posterior
Nested_sampling_algorithm
Multivariate generalization of the median
Timothy M. (2004), "An optimal randomized algorithm for maximum Tukey depth", Proc. 15th ACM–SIAM Symp. on Discrete Algorithms (SODA 2004), Society for Industrial
Centerpoint_(geometry)
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
Algorithm for pseudo-random number sampling
The ziggurat algorithm is an algorithm for pseudo-random number sampling. Belonging to the class of rejection sampling algorithms, it relies on an underlying
Ziggurat_algorithm
Algorithm used for pathfinding and graph traversal
A* (pronounced "A-star") is a graph traversal and pathfinding algorithm that is used in many fields of computer science due to its completeness, optimality
A*_search_algorithm
theoretic method for proving that a random process terminates, originally used by Robin Moser to prove an algorithmic version of the Lovász local lemma
Entropy_compression
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RANDOMIZED ALGORITHM
RANDOMIZED ALGORITHM
RANDOMIZED ALGORITHM
RANDOMIZED ALGORITHM
RANDOMIZED ALGORITHM
RANDOMIZED ALGORITHM
RANDOMIZED ALGORITHM
RANDOMIZED ALGORITHM
RANDOMIZED ALGORITHM
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