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Measure of algorithm performance for large inputs
In computer science, an algorithm is said to be asymptotically optimal if, roughly speaking, for large inputs it performs at worst a constant factor (independent
Asymptotically optimal algorithm
Asymptotically_optimal_algorithm
Sequence of operations for a task
(hopefully) asymptotically optimal algorithms. The goal is to find a reducing algorithm whose complexity is not dominated by the resulting reduced algorithms. For
Algorithm
Measurement of computational complexity
resources, asymptotic time complexity and asymptotic space complexity of computational algorithms and programs are commonly estimated. Other asymptotically estimated
Asymptotic computational complexity
Asymptotic_computational_complexity
Asymptotically optimal algorithm for a decision theory problem
Kullback–Leibler Upper Confidence Bound) is a UCB-type algorithm that is asymptotically optimal, in the sense that its regret matches the problem-dependent
Kullback–Leibler Upper Confidence Bound
Kullback–Leibler_Upper_Confidence_Bound
Algorithm that arranges lists in order
sorting algorithms around 1951 was Betty Holberton, who worked on ENIAC and UNIVAC. Bubble sort was analyzed as early as 1956. Asymptotically optimal algorithms
Sorting_algorithm
American computer scientist (born 1984)
Johnson-Lindenstrauss Transform (with Daniel Kane), and an asymptotically optimal algorithm for the count-distinct problem (with Daniel Kane and David
Jelani_Nelson
Algorithm for finding shortest paths
instance-optimal, meaning no correct algorithm can asymptotically relax fewer edges on the same graph instance. Although Dijkstra's algorithm is optimal for
Dijkstra's_algorithm
Algorithm to multiply matrices
Better asymptotic bounds on the time required to multiply matrices have been known since the Strassen's algorithm in the 1960s, but the optimal time (that
Matrix multiplication algorithm
Matrix_multiplication_algorithm
Recursive algorithm for matrix multiplication
algorithm was not optimal. The Strassen algorithm's publication resulted in more research about matrix multiplication that led to both asymptotically
Strassen_algorithm
Algorithm for computing relational joins
applying binary joins. Worst-case optimal join algorithms are asymptotically faster in worst case than any join algorithm based on such iterated binary joins
Worst-case optimal join algorithm
Worst-case_optimal_join_algorithm
Quantum search algorithm
Grover's algorithm is asymptotically optimal. Since classical algorithms for NP-complete problems require exponentially many steps, and Grover's algorithm provides
Grover's_algorithm
Mathematical and computational problem
optimal solutions to very large instances of the problem can be produced with sophisticated algorithms. In addition, many approximation algorithms exist
Bin_packing_problem
Fast approximate median algorithm
approximate median-selection algorithm that helps building an asymptotically optimal, exact general selection algorithm (especially in the sense of worst-case
Median_of_medians
Quantum algorithm for integer factorization
in complexity class BQP. Shor's algorithm is asymptotically faster than the most scalable classical factoring algorithm, the general number field sieve
Shor's_algorithm
Algorithm for integer multiplication
Kolmogorov conjectured that the traditional algorithm was asymptotically optimal, meaning that any algorithm for that task would require Ω ( n 2 ) {\displaystyle
Karatsuba_algorithm
Method for finding minimum spanning trees
In computer science, Prim's algorithm is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph. This means it finds a
Prim's_algorithm
I/O-efficient algorithm regardless of cache size
explicit parameter. An optimal cache-oblivious algorithm is a cache-oblivious algorithm that uses the cache optimally (in an asymptotic sense, ignoring constant
Cache-oblivious_algorithm
Classification of algorithm
multiplication usually make these algorithms impractical." Claude Shannon showed a simple but asymptotically optimal code that can reach the theoretical
Galactic_algorithm
Optimization theory in computing
Counter is asymptotically optimal amongst all algorithms for the problem. The algorithm is considered one of the precursors of streaming algorithms, and the
Approximate counting algorithm
Approximate_counting_algorithm
Describes approximate behavior of a function
formula Asymptotically optimal algorithm: A phrase frequently used to describe an algorithm that has an upper bound asymptotically within a constant of
Big_O_notation
Class of algorithms operating on data streams
first algorithm for it was proposed by Flajolet and Martin. In 2010, Daniel Kane, Jelani Nelson and David Woodruff found an asymptotically optimal algorithm
Streaming_algorithm
Class of algorithms that find approximate solutions to optimization problems
guarantees on the distance of the returned solution to the optimal one. Approximation algorithms naturally arise in the field of theoretical computer science
Approximation_algorithm
Search algorithm
When nodes are considered in a random order (i.e., the algorithm randomizes), asymptotically, the expected number of nodes evaluated in uniform trees
Alpha–beta_pruning
primarily applying another algorithm, such as merge sort or quicksort. Merge sort and quicksort are asymptotically optimal on large data, but the overhead
Hybrid_algorithm
American computer scientist
at MIT in 2007. His research contributions include an asymptotically optimal streaming algorithm for the count-distinct problem, which received the best
David_P._Woodruff
Non-parametric classification method
In statistics, the k-nearest neighbors algorithm (k-NN) is a non-parametric supervised learning method. It was first developed by Evelyn Fix and Joseph
K-nearest_neighbors_algorithm
Algorithm for shuffling a finite sequence
parallel algorithm with linear work and polylogarithmic depth. The asymptotic time and space complexity of the Fisher–Yates shuffle are optimal. Combined
Fisher–Yates_shuffle
Monte Carlo algorithm
Gagnon, Philippe (2022-04-15). "Optimal scaling of random walk Metropolis algorithms using Bayesian large-sample asymptotics". Statistics and Computing. 32
Metropolis–Hastings_algorithm
Multi-armed bandit sequential game
\ln(1/\delta )} as δ → 0 {\displaystyle \delta \to 0} , an algorithm is called asymptotically optimal if lim δ → 0 E [ τ δ ] ln ( 1 / δ ) = C ⋆ . {\displaystyle
Best_arm_identification
Mathematical algorithm
The Gauss–Newton algorithm is used to solve non-linear least squares problems, which is equivalent to minimizing a sum of squared function values. It
Gauss–Newton_algorithm
Algorithms for processing data too large to fit into a computer's main memory at once
running time possible for these operations, so using a B-tree is asymptotically optimal. External sorting is sorting in an external memory setting. External
External_memory_algorithm
Finds likely sequence of hidden states
(April 1967). "Error bounds for convolutional codes and an asymptotically optimum decoding algorithm". IEEE Transactions on Information Theory. 13 (2): 260–269
Viterbi_algorithm
Lower bound for bandit problem
"An Asymptotically Optimal Bandit Algorithm for Bounded Support Models". COLT. pp. 67–79. Riou, Charles; Honda, Junya (2020). "Bandit Algorithms Based
Lai–Robbins_lower_bound
Schönhage–Strassen algorithm: an asymptotically fast multiplication algorithm for large integers Toom–Cook multiplication: (Toom3) a multiplication algorithm for large
List_of_algorithms
Agreement algorithm
robust set estimation methods. Marzullo's algorithm is efficient in terms of time for producing an optimal value from a set of estimates with confidence
Marzullo's_algorithm
in ). Despite this, the algorithm is very powerful in that a random graph will be identified by the algorithm asymptotically almost surely. Even stronger
Colour_refinement_algorithm
Fast Fourier Transform algorithm
The Cooley–Tukey algorithm, named after J. W. Cooley and John Tukey, is the most common fast Fourier transform (FFT) algorithm. It re-expresses the discrete
Cooley–Tukey_FFT_algorithm
Optimized algorithm for computing the convex hull of a set of points
focused on instance-optimality and universal optimality. Instance-optimality: This concept relates to finding algorithms that are optimal for a specific set
Kirkpatrick–Seidel_algorithm
Algorithms which recursively solve subproblems
In computer science, divide and conquer is an algorithm design paradigm. A divide-and-conquer algorithm recursively breaks down a problem into two or
Divide-and-conquer_algorithm
Algorithm for the multi-armed bandit problem
Divergence) is an algorithm developed in 2015 by Junya Honda and Akimichi Takemura. It is the first algorithm proved to be asymptotically optimal respect to
Algorithm_IMED
NP-hard problem in combinatorial optimization
Christofides–Serdyukov algorithm yields a solution that, in the worst case, is at most 1.5 times longer than the optimal solution. As the algorithm was simple and
Travelling_salesman_problem
Method of finding a directed graph's strongly connected components
Kosaraju's algorithm performs two complete traversals of the graph and so runs in Θ(V+E) (linear) time, which is asymptotically optimal because there
Kosaraju's_algorithm
Class of algorithms in computational geometry
number of points in the hull). Such algorithms are called output-sensitive algorithms. They may be asymptotically more efficient than Θ ( n log n )
Convex_hull_algorithms
Family of iterative methods
of Θ {\textstyle \Theta } , then the Robbins–Monro algorithm will achieve the asymptotically optimal convergence rate, with respect to the objective function
Stochastic_approximation
Form of Newton's method used in statistics
(the correction after a single step) is 'optimal' in the sense that its error distribution is asymptotically identical to that of the true max-likelihood
Scoring_algorithm
referred to as data complexity), this means that the algorithm's worst-case running time is asymptotically the same as reading the input and writing the output
Yannakakis_algorithm
Tool for analyzing divide-and-conquer algorithms
In the analysis of algorithms, the master theorem for divide-and-conquer recurrences provides an asymptotic analysis for many recurrence relations that
Master theorem (analysis of algorithms)
Master_theorem_(analysis_of_algorithms)
Resource problem in machine learning
optimal solutions (not just asymptotically) using dynamic programming in the paper "Optimal Policy for Bernoulli Bandits: Computation and Algorithm Gauge
Multi-armed_bandit
Problem of finding obscured edges in a wire-frame 3D model
the running time is asymptotically greater than Θ(n2), the sequential complexity of the problem, the algorithm is not work-optimal, but it demonstrates
Hidden-line_removal
n)} ). Thus using Fibonacci heaps the total runtime of Prim's algorithm is asymptotically in O ( m + n log n ) {\displaystyle O(m+n\log n)} . It is important
Parallel algorithms for minimum spanning trees
Parallel_algorithms_for_minimum_spanning_trees
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
Numerical eigenvalue calculation
together have m 2 {\displaystyle m^{2}} elements, this is asymptotically optimal. Even algorithms whose convergence rates are unaffected by unitary transformations
Lanczos_algorithm
Algorithm for fast exponentiation
multiplications never grows more slowly than Θ(log n), so these algorithms improve asymptotically upon exponentiation by squaring by only a constant factor
Exponentiation_by_squaring
Algorithm to multiply two numbers
N-1}^{N}z_{i}\end{aligned}}} Karatsuba's algorithm was the first known algorithm for multiplication that is asymptotically faster than long multiplication, and
Multiplication_algorithm
Discrete Fourier transform algorithm
one-dimensional FFTs along the n1 direction. More generally, an asymptotically optimal cache-oblivious algorithm consists of recursively dividing the dimensions into
Fast_Fourier_transform
Mathematical problem involving optimal stopping theory
shortest rigorous proof known so far is provided by the odds algorithm. It implies that the optimal win probability is always at least 1 / e {\displaystyle
Secretary_problem
Field of machine learning
the theory of optimal control, which is concerned mostly with the existence and characterization of optimal solutions, and algorithms for their exact
Reinforcement_learning
Algorithm for searching sorted, infinite lists
(also called doubling search or galloping search or Struzik search) is an algorithm, created by Jon Bentley and Andrew Chi-Chih Yao in 1976, for searching
Exponential_search
The package-merge algorithm is an O(nL)-time algorithm for finding an optimal length-limited Huffman code for a given distribution on a given alphabet
Package-merge_algorithm
Node ordering for directed acyclic graphs
databases. The usual algorithms for topological sorting have running time linear in the number of nodes plus the number of edges, asymptotically, O ( | V | +
Topological_sorting
are two famous algorithms to achieve asymptotically optimal packing in k-uniform hypergraphs. One of them is a random greedy algorithm which was proposed
Packing_in_a_hypergraph
Complexity class of approximable problems
have efficient algorithms that can find an answer within some fixed multiplicative factor of the optimal answer. An approximation algorithm is called an
APX
Description of limiting behavior of a function
asymptotically equivalent functions to be freely exchanged in many algebraic expressions. Asymptotically equivalent functions remain asymptotically equivalent
Asymptotic_analysis
Mathematical model for sequential decision making under uncertainty
above is called an optimal policy and is usually denoted π ∗ {\displaystyle \pi ^{*}} . A particular MDP may have multiple distinct optimal policies. Because
Markov_decision_process
Hybrid sorting algorithm
introspective sort is a hybrid sorting algorithm that provides both fast average performance and (asymptotically) optimal worst-case performance. It begins
Introsort
Data structure for storing non-overlapping sets
forests are both asymptotically optimal and practically efficient. Disjoint-set data structures play a key role in Kruskal's algorithm for finding the
Disjoint-set_data_structure
key-independent optimality if, when randomly assigning the keys, the expected performance of the data structure is within a constant factor of the optimal data structure
Key-independent_optimality
Lossless data compression algorithms
sequence grows to infinity. In this sense an algorithm based on this scheme produces asymptotically optimal encodings. This result can be proven more directly
LZ77_and_LZ78
Problem in computer science
holds the logical OR of all hashed values. The first asymptotically space- and time-optimal algorithm for this problem was given by Daniel M. Kane, Jelani
Count-distinct_problem
Computer science problem
this optimal procedure has variance approximately equal to 2 n / 3 , {\displaystyle {\sqrt {2n}}/3,} and its limiting distribution is asymptotically normal
Longest increasing subsequence
Longest_increasing_subsequence
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 the multi-armed bandit problem
Explore Then Commit (ETC) is an algorithm for the multi-armed bandit problem focused on finding the best trade-off between exploration and exploitation
Explore-then-commit_algorithm
Machine learning technique
model and the objective is to minimize the algorithm's regret (the difference in performance compared to an optimal agent), it has been shown that an optimistic
Reinforcement learning from human feedback
Reinforcement_learning_from_human_feedback
Amount of resources to perform an algorithm
number of comparisons needed for a sorting algorithm. Thus the best sorting algorithms are asymptotically optimal, as their complexity is O ( n log n )
Computational_complexity
Sweep line algorithm
Although asymptotically faster algorithms are now known by Chazelle & Edelsbrunner (1992) and Balaban (1995), the Bentley–Ottmann algorithm remains a
Bentley–Ottmann_algorithm
Randomized algorithm
item of the input, including the items that are discarded. The algorithm's asymptotic running time is thus O ( n ) {\displaystyle O(n)} . Generating this
Reservoir_sampling
Computer science concept
In computer science, an optimal binary search tree (Optimal BST), sometimes called a weight-balanced binary tree, is a binary search tree which provides
Optimal_binary_search_tree
Voronoi tessellation where the generating point of each Voronoi cell is also its centroid
mass). It can be viewed as an optimal partition corresponding to an optimal distribution of generators. A number of algorithms can be used to generate centroidal
Centroidal Voronoi tessellation
Centroidal_Voronoi_tessellation
Measure of parallel computing efficacy
used to solve a particular problem. A parallel algorithm is considered cost efficient if its asymptotic running time multiplied by the number of processing
Cost_efficiency
Overview of and topical guide to algorithms
problems with overlapping subproblems and optimal substructure Greedy algorithm — algorithm that makes locally optimal choices Backtracking — search technique
Outline_of_algorithms
Computational geometry problem
this statement. This algorithm, based on sorting the intervals, was later shown by Michael Fredman and Bruce Weide (1978) to be optimal. Later in 1977, Jon
Klee's_measure_problem
Parsing algorithm for context-free grammars
efficient [citation needed] parsing algorithms in terms of worst-case asymptotic complexity, although other algorithms exist with better average running
CYK_algorithm
Divide and conquer sorting algorithm
one of the first sorting algorithms where optimal speed up was achieved, with Richard Cole using a clever subsampling algorithm to ensure O(1) merge. Other
Merge_sort
Algorithm for solving the partition problem
complexity of this algorithm is dominated by the step 1 (sorting), which takes O(n log n). Note that this partition is not optimal: in the partition {8
Largest_differencing_method
Ancient algorithm for generating prime numbers
In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking
Sieve_of_Eratosthenes
Parameter-free superresolution algorithm
SAMV (iterative sparse asymptotic minimum variance) is a parameter-free superresolution algorithm for the linear inverse problem in spectral estimation
SAMV_(algorithm)
Sorting algorithm
simulating Mehlhorn's algorithm for computing nearly optimal binary search trees with low overhead, thereby achieving optimal adaptivity up to an additive
Powersort
Any node-based binary search tree that automatically keeps its height the same
simple-to-describe yet asymptotically optimal O ( n log n ) {\displaystyle O(n\log n)} sorting algorithm. Similarly, many algorithms in computational geometry
Self-balancing binary search tree
Self-balancing_binary_search_tree
Sequence in computer science
work-inefficient—it performs asymptotically more work (a logarithmic factor) than is required sequentially. Consequently, Algorithm 1 is likely to perform better
Prefix_sum
Optimization problem
Optimal facility location (OFL), also called location analysis, is a class of optimization problems. In all these problems, the goal is to decide where
Optimal_facility_location
Operations research problem of packing items into the largest number of bins
distributions, and a learning algorithm with asymptotically optimal expected behavior for all discrete distributions. An asymptotic FPTAS. Csirik, Frenk, Lebbe
Bin_covering_problem
Experimental design that is optimal with respect to some statistical criterion
same precision as an optimal design. In practical terms, optimal experiments can reduce the costs of experimentation. The optimality of a design depends
Optimal_experimental_design
Algorithmic runtime requirements for matrix multiplication
of January 2024[update], the best bound on the asymptotic complexity of a matrix multiplication algorithm is O(n2.371339). However, this and similar improvements
Computational complexity of matrix multiplication
Computational_complexity_of_matrix_multiplication
Trail in a graph that visits each edge once
are also used in CMOS circuit design to find an optimal logic gate ordering. There are some algorithms for processing trees that rely on an Euler tour
Eulerian_path
Decodes a bitstream with the Viterbi algorithm
the paper "Error Bounds for Convolutional Codes and an Asymptotically Optimum Decoding Algorithm". There are both hardware (in modems) and software implementations
Viterbi_decoder
Optimization algorithm
convergence rate bound of the heavy ball method is asymptotically the same as that for the optimal conjugate gradient method. This technique is used in
Gradient_descent
Algorithm that estimates unknowns from a series of measurements over time
theory, Kalman filtering (also known as linear quadratic estimation) is an algorithm that uses a series of measurements observed over time, including statistical
Kalman_filter
Algorithm for computing convex hulls in a set of points
gift wrapping algorithm is an algorithm for computing the convex hull of a given set of points. In the two-dimensional case the algorithm is also known
Gift_wrapping_algorithm
Algorithm in graph theory
Floyd–Warshall algorithm (also known as Floyd's algorithm, the Roy–Warshall algorithm, the Roy–Floyd algorithm, or the WFI algorithm) is an algorithm for finding
Floyd–Warshall_algorithm
Statistics and machine learning technique
Bayes optimal classifier represents a hypothesis that is not necessarily in H {\displaystyle H} . The hypothesis represented by the Bayes optimal classifier
Ensemble_learning
ASYMPTOTICALLY OPTIMAL-ALGORITHM
ASYMPTOTICALLY OPTIMAL-ALGORITHM
Girl/Female
Tamil
Boy/Male
Hindu, Indian, Marathi
The Primal God
Girl/Female
Hindu, Indian
The Primal Energy
Girl/Female
Hindu, Indian, Traditional
The Primal Lakshmi
Girl/Female
Hindu, Indian
The Primal Mother
Boy/Male
Hindu
The primal God
Boy/Male
Tamil
The primal God
Boy/Male
Arabic, Muslim
First; New; Another Name for God; Novel; Primal
Boy/Male
Indian, Sanskrit
The Primal Idol
Boy/Male
Tamil
To do something systematically, Optimum utilization of resources
Boy/Male
Indian, Sanskrit
One God; The Primal God
Girl/Female
Indian
Optional
Boy/Male
Indian, Sanskrit
The Primal Root
Boy/Male
Hindu
To do something systematically, Optimum utilization of resources
Boy/Male
Indian, Sanskrit
The Primal Residue
Girl/Female
Hindu
Girl/Female
Hindu, Indian
Primal; A Wife of Agni
Boy/Male
Gujarati, Hindu, Indian, Kannada, Marathi, Punjabi, Sikh
Lord Shiva; God's Name; Primal Being
Boy/Male
Hindu, Indian
To do Something Systematically or Optimum Utilization of Resources
Boy/Male
Indian, Sanskrit
The Primal Head of Religious Sacrifice
ASYMPTOTICALLY OPTIMAL-ALGORITHM
ASYMPTOTICALLY OPTIMAL-ALGORITHM
Female
French
Old French name RIVA means "bank, coast." Compare with another form of Riva.
Girl/Female
Spanish
Beautiful.
Female
English
Pet form of English Minta, MINTY means "mint."Â
Boy/Male
Indian
One that divides into two, Creator
Boy/Male
Tamil
Full of knowledge, Embodied with knowledge
Girl/Female
American, British, English
Bright Fame; Famous
Surname or Lastname
English
English : variant of Jackman.
Boy/Male
British, English
From the West Farm
Boy/Male
Arabic, Muslim, Parsi, Sindhi
Handsome; Elegant; Graceful; Well Proportioned
Boy/Male
Bengali, Hindu, Indian
Lord Shiva
ASYMPTOTICALLY OPTIMAL-ALGORITHM
ASYMPTOTICALLY OPTIMAL-ALGORITHM
ASYMPTOTICALLY OPTIMAL-ALGORITHM
ASYMPTOTICALLY OPTIMAL-ALGORITHM
ASYMPTOTICALLY OPTIMAL-ALGORITHM
n.
An optical toy similar to the phenakistoscope. See Phenakistoscope.
n.
Government by the nobility.
n.
See Elective, n.
n.
An instrument for showing the optical effects of color.
n.
A nobleman or aristocrat; a chief man in a state or city.
n.
An optical glass that is convex on both sides.
a.
Of or pertaining to the nobility or aristocracy.
a.
One who deals in optical glasses and instruments.
n.
A reflecting optical glass or instrument; a mirror.
a.
Relating to the science of optics; as, optical works.
adv.
In an optional manner.
n.
Of or pertaining to the science of vision; optical.
n.
One of those who stand in the second rank of honors, immediately after the wranglers, in the University of Cambridge, England. They are divided into senior and junior optimes.
a.
Alt. of Optical
n.
Collectively, the nobility.
a.
Of or pertaining to the eye; ocular; as, the optic nerves (the first pair of cranial nerves) which are distributed to the retina. See Illust. of Brain, and Eye.
n.
The space covered by an optical instrument at one view.
a.
Of or pertaining to vision or sight.
n.
An optical glass; a telescope.
a.
Involving an option; depending on the exercise of an option; left to one's discretion or choice; not compulsory; as, optional studies; it is optional with you to go or stay.