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Algorithm for searching sorted, infinite lists
In computer science, an exponential search (also called doubling search or galloping search or Struzik search) is an algorithm, created by Jon Bentley
Exponential_search
Search algorithm used in sorted arrays
solves a number of search problems in computational geometry and in numerous other fields. Exponential search extends binary search to unbounded lists
Binary_search
Algorithmic search method
An exponential tree is a type of search tree where the number of children of its nodes decreases doubly-exponentially with increasing depth. Values are
Exponential_tree
Estimate of time taken for running an algorithm
an exponential. In this sense, problems that have sub-exponential time algorithms are somewhat more tractable than those that only have exponential algorithms
Time_complexity
trees in O ( log w n ) {\displaystyle O(\log _{w}n)} time. Using exponential search trees, a query can be performed in O ( log n / log log n ) {\displaystyle
Word_RAM
Growth of quantities at rate proportional to the current amount
Exponential growth occurs when a quantity grows as an exponential function of time. The quantity grows at a rate directly proportional to its present
Exponential_growth
Heuristic search algorithm for evaluating game trees
heuristic search in the field of automated theorem proving by W. Ertel, J. Schumann and C. Suttner in 1989, thus improving the exponential search times of
Monte_Carlo_tree_search
On finding a repeating loop in a sequence
values. Alternatively, Brent's algorithm is based on the idea of exponential search. Both Floyd's and Brent's algorithms use only a constant number of
Cycle_detection
Algorithm for finding the extrema of a unimodal function
Binary search algorithm (can be used to search for where the derivative changes in sign) Interpolation search Exponential search Linear search "Ternary
Ternary_search
Quantum search algorithm
require exponentially many steps, and Grover's algorithm provides at most a quadratic speedup over the classical solution for unstructured search, this
Grover's_algorithm
Sorting algorithm in Python
two adjacent runs into a single one using a “galloping strategy”: exponential search is used to find the prefix of one run that precedes the minimum in
Powersort
Heuristic pathfinding algorithm
conclude that compared to a brute-force tree search over an exponential-sized problem, IDA* achieves a smaller search depth (by a constant factor), but not a
Iterative_deepening_A*
Difficulties arising when analyzing data with many aspects ("dimensions")
semantic meaning Exponential search space: the search space can no longer be systematically scanned Data snooping bias: given the large search space, for every
Curse_of_dimensionality
Hybrid sorting algorithm based on insertion sort and merge sort
two-stage search for the place in the run R1 where the next element x of the run R2 would be inserted. In the first stage it performs an exponential search, also
Timsort
Canadian search engine
Million Short is a web search engine from Toronto-based startup Exponential Labs. The search engine, which brands itself as “more of a discovery engine
Million_Short
Software that systematically browses the World Wide Web
Web and that is typically operated by search engines for the purpose of Web indexing (web spidering). Web search engines and some other websites use web
Web_crawler
Algorithm used for pathfinding and graph traversal
in certain contrived situations where the edge weight of the search graph is exponential in the size of the graph and that certain inconsistent (but admissible)
A*_search_algorithm
Overview of and topical guide to algorithms
Linear search Binary search algorithm Interpolation search Exponential search Jump search Depth-first search Breadth-first search Best-first search Beam
Outline_of_algorithms
Searching algorithm
numerical values of the keys increase exponentially) it can make up to O(n) comparisons. In interpolation-sequential search, interpolation is used to find an
Interpolation_search
Base of natural logarithms
mathematical constant that is the base of the natural logarithm and exponential function. It is approximately equal to 2.718281828459045235360287471352
E_(mathematical_constant)
Approximate nearest neighbor search algorithm
navigable small world (HNSW) is an algorithm for approximate nearest neighbor search. It is used to find items that are similar to a query item in a large collection
Hierarchical navigable small world
Hierarchical_navigable_small_world
Intelligence in machines
because they experienced a "combinatorial explosion", meaning they become exponentially slower as the problems grow. Even humans rarely use the step-by-step
Artificial_intelligence
Unproven computational hardness assumption
In computational complexity theory, the exponential time hypothesis or ETH is an unproven computational hardness assumption that was formulated by Impagliazzo
Exponential_time_hypothesis
Free online crowdsourced encyclopedia
domain from wikipedia.com to wikipedia.org. After an early period of exponential growth, the growth rate of the English Wikipedia in terms of the numbers
Wikipedia
Describes the sum of independent normal and exponential random variables
an exponentially modified Gaussian distribution (EMG, also known as exGaussian distribution) describes the sum of independent normal and exponential random
Exponentially modified Gaussian distribution
Exponentially_modified_Gaussian_distribution
regions. This reduces the data produced and also does not require exponential search time. Yet it is not feasible to apply the PCA method to large chromosomal
Tag_SNP
Data structure for storing integers from a bounded domain
space usage of x-fast tries in practice. By using an exponential search before the binary search over the levels and by querying not only the current
X-fast_trie
Query of largest element in a set less than an element
Andersson, Arne; Thorup, Mikkel (2007), "Dynamic ordered sets with exponential search trees", Journal of the ACM, 54 (3): A13, arXiv:cs/0210006, doi:10
Predecessor_problem
by using an outer level of exponential search or sequential search for the optimal choice of k, with each step of the search based on the same iterative
Iterative_compression
Method of data analysis
human-into-the-algorithmic-loop: Human domain expertise can help to reduce an exponential search space through heuristic selection of samples. This can be beneficial
Clustering high-dimensional data
Clustering_high-dimensional_data
Growth at a rate that is a logarithmic function
multiplying by a fixed constant. Logarithmic growth is the inverse of exponential growth and is very slow. A familiar example of logarithmic growth is
Logarithmic_growth
Logarithm to the base of the mathematical constant e
function of a positive real variable, is the inverse function of the exponential function, leading to the identities: e ln x = x if x ∈ R + ln e
Natural_logarithm
Search algorithm
during the search if the move ordering is incorrect, each time leading to inefficiency. As the number of positions searched decreases exponentially each move
Alpha–beta_pruning
Algorithm for finding shortest paths
savings can be dramatic, sometimes reducing the explored region from an exponential-size ball to two smaller half-balls. The method is widely used in point-to-point
Dijkstra's_algorithm
carefully controlled; its time increases exponentially as the lookahead limit increases. More sophisticated search techniques such as alpha–beta pruning
Combinatorial_search
Indo-Canadian serial entrepreneur, angel investor and author
Founding Executive Director of Singularity University and lead author of Exponential Organizations. In March 2017 he was named to the board of the XPRIZE
Salim_Ismail
Problem-solving technique and algorithmic paradigm
In computer science, brute-force search or exhaustive search, also known as generate and test, is a very general problem-solving technique and algorithmic
Brute-force_search
American social networking service
"While the amount of CSE (child sexual exploitation) online has grown exponentially, Twitter's investment in technologies to detect and manage the growth
X_(social_network)
Type of machine learning model
}}\Pr({\text{correct token}})} , then ( log x , y ) {\displaystyle (\log x,y)} is an exponential curve (before it hits the plateau at one), which looks like emergence
Large_language_model
Andersson, Arne; Thorup, Mikkel (2007), "Dynamic ordered sets with exponential search trees", Journal of the ACM, 54 (3): A13, arXiv:cs/0210006, doi:10
Fusion_tree
Numerical optimization method
searching space, e.g. a confounded design with exponentially distributed spacings/steps. This search goes on sequentially on each parameter and refines
Random_search
Cryptanalytic method for unauthorized users to access data
because a brute-force search takes too long. Longer passwords, passphrases and keys have more possible values, making them exponentially more difficult to
Brute-force_attack
Concept involving online bot activity
maneuvered ourselves into. Decoupled, proliferated, and in a state of exponential metastasis. — Thomas Sommerer Facebook includes an option to provide
Dead_Internet_theory
Mathematical optimization technique
solution. For a very large-scale neighborhood search, the neighborhood is large and possibly exponentially sized. The resulting algorithms can outperform
Very large-scale neighborhood search
Very_large-scale_neighborhood_search
Compact astronomical body
associated with a parameter dictating the black hole's internal mass growing exponentially, and the buildup of tidal forces is called the mass-inflation singularity
Black_hole
Technique for producing oligonucleotides that specifically bind to a target
Systematic evolution of ligands by exponential enrichment (SELEX), also referred to as in vitro selection or in vitro evolution, is a combinatorial chemistry
Systematic evolution of ligands by exponential enrichment
Systematic_evolution_of_ligands_by_exponential_enrichment
Japanese television series
gives a man a fox who helps him in business, but the fox demands an exponential price in return. A stonecutter learns who the most important man in the
Folktales_from_Japan
Optimized search algorithm
Bidirectional search is a graph search algorithm that finds a shortest path from an initial vertex to a goal vertex in a directed graph. It runs two simultaneous
Bidirectional_search
Describes approximate behavior of a function
terms are summarized in a single big O term. Consider, for example, the exponential series and two expressions of it that are valid when x {\displaystyle
Big_O_notation
Probabilistic problem-solving algorithm
to a degree of freedom. Monte Carlo methods provide a way out of this exponential increase in computation time. As long as the function in question is
Monte_Carlo_method
Measure of a civilization's evolution
D. (1985). "Exponential Expansion: Galactic Destiny or Technological Hubris?". In Finney, B. R.; Papagiannis, M. D. (eds.). The Search for Extraterrestrial
Kardashev_scale
Factorization algorithm
to search for smooth numbers (i.e. numbers with small prime factors) of order n {\displaystyle {\sqrt {n}}} . The size of these values is exponential in
General_number_field_sieve
Mathematical function, inverse of an exponential function
inverse of the complex exponential function. Similarly, the discrete logarithm is the multi-valued inverse of the exponential function in finite groups;
Logarithm
Open problem on 3x+1 and x/2 functions
As k increases, the search only needs to check those residues b that are not eliminated by lower values of k. Only an exponentially small fraction of the
Collatz_conjecture
Experiment methodology
test in 2000 to determine the optimum number of results to display in its search-engine results. The first test was unsuccessful because of glitches that
A/B_testing
Third planet from the Sun
remains limited. Since the 19th century, the human population has grown exponentially to eight billion in the 2020s, and is projected to peak at around ten
Earth
Tree structure in information science
Z-value which is in the multidimensional search range. The original algorithm to solve this key problem was exponential with the dimensionality and thus not
UB-tree
complete search algorithms finding the optimal solution, vs. local search algorithms finding a local optimum. Search strategy - best-first search or depth-first
Distributed constraint optimization
Distributed_constraint_optimization
Method for problem solving in optimization
search-spaces: Luus–Jaakola searches locally using a uniform distribution and an exponentially decreasing search-range. Random optimization searches locally using a
Local_search_(optimization)
Family of numerical optimization methods
current position and uses a simple formula for exponentially decreasing the sampling range. Random search is a related family of optimization methods that
Pattern_search_(optimization)
Country in West Africa
in Nigeria. Since 2000, Chinese–Nigerian trade relations have risen exponentially. There has been an increase in total trade of over 10.3 billion dollars
Nigeria
Online database of integer sequences
sequence. The database is searchable by keyword, by subsequence, or by any of 16 fields. There is also an advanced search function called SuperSeeker
On-Line Encyclopedia of Integer Sequences
On-Line_Encyclopedia_of_Integer_Sequences
Period of rapid progress in AI
Google's Gemini. The popularity of text-to-video generative AI tools grew exponentially. With the release of models such as OpenAI's Sora in 2024, the use of
AI_boom
Polynomial equation whose integer solutions are sought
the sum of two or more unknowns, with coefficients, to a constant. An exponential Diophantine equation is one in which unknowns can appear in exponents
Diophantine_equation
List of unsolved computational problems
= RL problem Unique games conjecture Is the exponential time hypothesis true? Is the strong exponential time hypothesis (SETH) true? Do one-way functions
List of unsolved problems in computer science
List_of_unsolved_problems_in_computer_science
Capital city of Oklahoma, United States
of 2010. As a result of MAPS, the population in downtown housing has exponentially increased, with the demand for additional residential and retail amenities
Oklahoma_City
Study of health and disease within a population
Framework for an Emerging Set of Public Health Informatics Methods to Analyze Search, Communication and Publication Behavior on the Internet". Journal of Medical
Epidemiology
Armed conflict in the Middle East
it in 1991. The rate of militant recruitment in Yemen has increased exponentially. According to an international organization, between 26 March and 24
Yemeni civil war (2014–present)
Yemeni_civil_war_(2014–present)
Content management system
2025/08/25, 7x released a new version of the rebranded software stack Exponential 6.0.10 to encourage users to continue to use eZ Publish freely even under
EZ_Publish
Points with no three in a line
"perhaps, my favorite open problem" and gives a simplified proof of the exponential bound on cap sets, namely that for any prime power p {\displaystyle p}
Cap_set
Two-person zero-sum game
trajectory for problems of these types is always a geometric sequence (or exponential function for continuous problems). This result yields an easy method
Search_game
Elementary particle involved with rest mass
analysing whether it could also be the inflaton responsible for this exponential expansion of the universe during the Big Bang. Such theories are highly
Higgs_boson
Product of numbers from 1 to n
In mathematical analysis, factorials are used in power series for the exponential function and other functions, and they also have applications in algebra
Factorial
Computer science concept
{\displaystyle {2n \choose n}{\frac {1}{n+1}}} , which is exponential in n, brute-force search is not usually a feasible solution. In 1971, Knuth published
Optimal_binary_search_tree
2003 online virtual world platform
offers to its residents. At the same time, the service saw a period of exponential growth of its user base. One of the principal developers, Cory Ondrejka
Second_Life
Algorithm for manipulating images
{\displaystyle f(x,y)} by testing a sequence of candidate offsets at an exponentially decreasing distance from v 0 {\displaystyle v_{0}} u i = v 0 + w α i
PatchMatch
Artwork incorporating both painting and sculpture
subjectivity of art reception that postmodernism explores. Bois also considers the search for iconographic meaning in Rauschenberg's work misguided because it is
Combine_painting
Unit of information
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Data
French computer scientist and ufologist (born 1939)
Rice University Marks 10 years: Exploring supernatural encounters and exponential growth". KPRC-TV. Archived from the original on November 2, 2024. Clarke
Jacques_Vallée
Computer-based technologies
"data-in-transit rather than... data-at-rest". Hilbert and Lopez identify the exponential pace of technological change (a kind of Moore's law): machines' application-specific
Information_technology
American multinational retail corporation
2015. Kendall, Gerald I. (1998). Securing the future: strategies for exponential growth using the theory of constraints. Boca Raton, Florida: CRC Press
Walmart
Sequence of characters that forms a search pattern
concise—eliminating a single complement operator can cause a double exponential blow-up of its length. Regular expressions in this sense can express
Regular_expression
Regular expression denial-of-service attack
certain regex-input pairs, the time taken can grow polynomially or exponentially in relation to the input size. An attacker can thus cause a program
ReDoS
Unsolved problem in computer science
that solves the task and runs in polynomial time (as opposed to, say, exponential time), meaning the task completion time is bounded above by a polynomial
P_versus_NP_problem
Operating system for mobile devices
unauthorised third parties. Security threats on Android are reportedly growing exponentially; however, Google engineers have argued that the malware and virus threat
Android_(operating_system)
Type of AI with wide-ranging abilities
necessary hardware would be available sometime between 2015 and 2025, if the exponential growth in computer power at the time of writing continued. The Human
Artificial general intelligence
Artificial_general_intelligence
Data-interchange format
signed decimal number that may contain a fractional part and may use exponential E notation but cannot include non-numbers such as NaN. The format makes
JSON
Search engine website
site had more than one million hits. This number was growing almost exponentially and was later confirmed. Over time, Olé diversified its services to
Olé_(search_engine)
Abrahamic monotheistic religion
of Churches: Evangelical churches: "Evangelical churches have grown exponentially in the second half of the 20th century and continue to show great vitality
Christianity
NP-hard problem in combinatorial optimization
algorithm for the TSP increases superpolynomially (but no more than exponentially) with the number of cities. The problem was first formulated in 1930
Travelling_salesman_problem
Argentine writer (1899–1986)
imagine I would have felt as though I were installing something that exponentially increased what one day would be called bandwidth, though bandwidth of
Jorge_Luis_Borges
Disc-shaped analog sound storage medium
in recitals by proxy. The Orthophonic Victrola had an interior folded exponential horn, a sophisticated design informed by impedance-matching and transmission-line
Phonograph_record
further calling it a "genuine Chernobyl-level disaster that seems to get exponentially more radioactive as it goes along". Collider also referred to the film
List of 21st-century films considered the worst
List_of_21st-century_films_considered_the_worst
Earth's highest mountain
altitude alright, but the effect on the human body is disproportionate—an exponential curve. People climb Denali [6,190 m or 20,320 ft] or Aconcagua [6,960 m
Mount_Everest
Middle quantile of a data set or probability distribution
is the minimum value for which the power law holds. The median of an exponential distribution with rate parameter λ is the natural logarithm of 2 divided
Median
20th-century Italian saint, priest, stigmatist and mystic (1887–1968)
the Holy Eucharist without other nourishment. Padre Pio's fame grew exponentially among the wider populace. He became a spiritual director, and it was
Padre_Pio
Post-apocalyptic dystopian thriller TV series
wealth. The series star Daveed Diggs said that the show would "broaden exponentially" the world established by the film and the 1982 graphic novel. "That's
Snowpiercer_(TV_series)
Number, approximately 3.14
using properties of the complex exponential, exp z, of a complex variable z. Like the cosine, the complex exponential can be defined in one of several
Pi
Typographic character indicating a question (?)
mark function. In linear logic, the question mark denotes one of the exponential modalities that control weakening and contraction. When placed above
Question_mark
Star at the centre of the Solar System
The Sun does not have a definite boundary, but its density decreases exponentially with increasing height above the photosphere. For the purpose of measurement
Sun
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