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Type of function in linear algebra
In linear algebra, a sublinear function (or functional as is more often used in functional analysis), also called a quasi-seminorm, on a vector space
Sublinear_function
Topics referred to by the same term
up sublinear in Wiktionary, the free dictionary. Sublinear or sub-linear means 'below linear' or 'less than linear', and may refer to: Sublinear function
Sublinear
Estimate of time taken for running an algorithm
type of sublinear time algorithm is closely related to property testing and statistics. Other settings where algorithms can run in sublinear time include:
Time_complexity
Indian-American computer scientist
algorithms, hardness of approximation, combinatorial optimization, and sublinear algorithms. Khanna received his undergraduate degrees in computer science
Sanjeev_Khanna
Speed of convergence of a mathematical sequence
superlinearly (i.e., faster than linearly). A sequence is said to converge sublinearly (i.e., slower than linearly) if it converges and lim k → ∞ | x k + 1
Rate_of_convergence
Method for finding kth smallest value
it may be possible to perform selection in an amount of time that is sublinear in the number of values. As a simple case of this, for data already sorted
Selection_algorithm
Function in mathematical analysis
continuity that is either concave, or subadditive, or uniformly continuous, or sublinear (in the sense of growth). Actually, the existence of such special moduli
Modulus_of_continuity
Punctuation to signal the end of a sentence (.)
ARABIC FULL STOP U+0701 ܁ SYRIAC SUPRALINEAR FULL STOP U+0702 ܂ SYRIAC SUBLINEAR FULL STOP U+1362 ። ETHIOPIC FULL STOP U+166E ᙮ CANADIAN SYLLABICS FULL
Full_stop
Sequence of characters that forms a search pattern
match. GNU grep (and the underlying gnulib DFA) uses such a strategy. Sublinear runtime algorithms have been achieved using Boyer-Moore (BM) based algorithms
Regular_expression
Theorem on extension of bounded linear functionals
norm-preserving version with the dominated extension version that uses sublinear functions. Whereas Helly's proof used mathematical induction, Hahn and
Hahn–Banach_theorem
Hybrid sorting algorithm based on insertion sort and merge sort
technique derives from Carlsson, Levcopoulos, and O. Petersson's 1990 paper "Sublinear merging and natural merge sort" and Peter McIlroy's 1993 paper "Optimistic
Timsort
Function made from a set
nonnegative stands in contrast to other classes of functions, such as sublinear functions and real linear functionals, that do allow negative values.
Minkowski_functional
French musician (1912–2000)
there are 8 sublinear signs) and poetry (the three books, Psalms, Proverbs, and the poetic sections of Job in which there are 7 sublinear signs). She
Suzanne_Haïk-Vantoura
answer. For example, if an algorithm takes a set of data as input, and has sublinear runtime, then the same algorithm can be run repeatedly (or in parallel)
Median_trick
Algorithm for generating prime numbers
better asymptotic complexity, and was the first sieve with a running time sublinear in the specified bound. Its asymptotic running-time has not been improved
Sieve_of_Pritchard
Power law growth of entropy of language or a stochastic process
language texts or samples of particular stochastic processes grow as a sublinear power of the sample length, possibly in addition to the term that is linear
Hilberg's_hypothesis
Maximal subgraph whose vertices can reach each other
have been used to study algorithms with limited space complexity, and sublinear time algorithms can accurately estimate the number of components. A component
Component_(graph_theory)
Numbers whose differences are not squares
square-difference-free set of numbers up to n {\displaystyle n} is only slightly sublinear, but the largest known sets of this form are significantly smaller, of
Square-difference-free_set
Italian computer scientist (1971–2024)
checkable proofs, approximation, property testing, spectral graph theory, and sublinear algorithms. He also ran a blog, in theory, about theoretical computer
Luca_Trevisan
Mathematical function
a type of function called a sublinear function. A map p : X → R {\displaystyle p:X\to \mathbb {R} } is called a sublinear function if it is subadditive
Seminorm
Data structure
structure which gives substring search in a text or text collection in sublinear time. Once constructed from a document or set of documents, a substring
Substring_index
Length in a vector space
so that in particular, every norm is also a seminorm (and thus also a sublinear functional). However, there exist seminorms that are not norms. Properties
Norm_(mathematics)
Unicode character block
for U+0709 SYRIAC SUBLINEAR COLON SKEWED RIGHT L2/12-188 N4272 Anderson, Deborah (2012-05-08), Naming error for U+0709 SYRIAC SUBLINEAR COLON SKEWED RIGHT
Syriac_(Unicode_block)
Data structure
enables elements (or mappings) to be located, inserted, or deleted in sublinear time. In a beap, each element is stored in a node with up to two parents
Beap
Historical system of diacritics for Hebrew
longer in use in any Jewish community, having been supplanted by the sublinear Tiberian vocalization. However, the Babylonian pronunciation as reflected
Babylonian_vocalization
Research institute in Berkeley, California
Institute for the Theory of Computing. 2024-01-09. Retrieved 2024-01-14. "Sublinear Algorithms". Simons Institute for the Theory of Computing. 2024-05-20
Simons Institute for the Theory of Computing
Simons_Institute_for_the_Theory_of_Computing
Probabilistic data structure in computer science
differently and therefore sized differently: a count–min sketch typically has a sublinear number of cells, related to the desired approximation quality of the sketch
Count–min_sketch
Marks to indicate pacing of written text
other Syriac ܂ SYRIAC SUBLINEAR FULL STOP U+0702 Po, other Syriac ܃ SYRIAC SUPRALINEAR COLON U+0703 Po, other Syriac ܄ SYRIAC SUBLINEAR COLON U+0704 Po, other
Punctuation
Information retrieval using cryptography
Leonardos, Helger Lipmaa, Kateryna Pavlyk, Qiang Tang, in 2015. All previous sublinear-communication computational PIR protocol required linear computational
Private_information_retrieval
Cryptography secured against quantum computers
Zhen; Ma, Zhi; Wang, H.; Long, Gui-Lu (2022). "Factoring integers with sublinear resources on a superconducting quantum processor". arXiv:2212.12372 [quant-ph]
Post-quantum_cryptography
American computer scientist
American theoretical computer scientist. She is known for her research in sublinear-time algorithms, information privacy, property testing, and approximation
Sofya_Raskhodnikova
Set of distances defined from a set of points
non-integer in its distance set. Square grids of points have distance sets of sublinear size, in contrast to points in general position whose distance set is
Distance_set
Israeli theoretical computer scientist
testing, expander graphs, coding theory, and randomized algorithms with sublinear time complexity. She is a professor of computer science at Bar-Ilan University
Tali_Kaufman
Signed odd unit fractions sum to π/4
is correct. Leibniz's formula converges extremely slowly: it exhibits sublinear convergence. Calculating π to 10 correct decimal places using direct summation
Leibniz_formula_for_π
Cryptographic primitive
proposed. Under strong knowledge assumptions, it is known how to create sublinear-length computationally-sound proof systems for NP-complete languages.
Non-interactive zero-knowledge proof
Non-interactive_zero-knowledge_proof
Discrete Fourier transform algorithm
algorithm that uses sublinear samples 2 O ( d 2 ) k log n log log n {\displaystyle 2^{O(d^{2})}k\log n\log \log n} and sublinear decoding time k log
Sparse_Fourier_transform
Type of cryptography protocol
of the database entries. On the other hand, PIR requires communication sublinear in n, whereas 1-out-of-n oblivious transfer has no such requirement. However
Oblivious_transfer
American mathematician (1928–2021)
thesis On certain classes of function spaces and on the interpolation of sublinear operators. At DePaul University he became an instructor in 1955, an assistant
Guido_Weiss
Large connected component of a random graph
component and many small ones. At this edge probability, the large component is not yet a giant component: it contains only a sublinear number of vertices.
Giant_component
Greek computer scientist
fundamental contributions to algorithmic game theory, mechanism design, sublinear algorithms, and theoretical machine learning". Constantinos Daskalakis
Constantinos_Daskalakis
Searching for patterns in text
Knuth–Morris–Pratt Θ(m) Θ(n + o) Θ(m) Commentz-Walter Boyer-Moore Θ(m) Θ(M * n) worst case sublinear in average Θ(m) Set-BOM Backward Oracle Matching
String-searching_algorithm
Scoring of contract bridge
the standard IMP table below. The purpose of the IMP table, which has sublinear dependency on differences, is to reduce results occurring from large swings
Bridge_scoring
Ancient algorithm for generating prime numbers
" Sci. Comput. Programming 9:1 (1987), pp. 17–35. Paul Pritchard, "A sublinear additive sieve for finding prime numbers", Communications of the ACM 24
Sieve_of_Eratosthenes
Area of mathematics
Hahn–Banach theorem:—If p : V → R {\displaystyle p:V\to \mathbb {R} } is a sublinear function, and φ : U → R {\displaystyle \varphi :U\to \mathbb {R} } is
Functional_analysis
Israeli theoretical computer scientist
theoretical computer scientist known for her work on property testing and sublinear-time algorithms. She is a professor of computer science at the Academic
Michal_Parnas
English translation of the Bible
the CLNT, which is more idiomatic in its English than the hyper-literal sublinear. The CLNT and the Concordant Greek Text are linked together and correlated
Concordant_Version
Varying methods used to calculate pi
log n ) 2 ) {\displaystyle O(M(n)(\log n)^{2})} Leibniz formula for π 1300s Sublinear convergence. Five billion terms for 10 correct decimal places
Approximations_of_pi
Mathematical function often applied to matrices
M[\gamma \,A]=\gamma \cdot M[A],\qquad \gamma \in \mathbb {R} ^{+}} Sublinearity M [ A + B ] ≤ M [ A ] + M [ B ] {\displaystyle \,M[A+B]\,\leq \,M[A]+M[B]}
Logarithmic_norm
Israeli mathematician
Itai; Kalai, Gil; Schramm, Oded (2003), "First passage percolation has sublinear distance variance", Ann. Probab., 31 (4): 197–1978, arXiv:math/0203262
Itai_Benjamini
Low-space search for a majority element
actually a majority. This second pass is needed, as it is not possible for a sublinear-space algorithm to determine whether there exists a majority element in
Boyer–Moore majority vote algorithm
Boyer–Moore_majority_vote_algorithm
Resource problem in machine learning
Srikant, R.; Liu, Xin; Jiang, Chong (2015), "Algorithms with Logarithmic or Sublinear Regret for Constrained Contextual Bandits", The 29th Annual Conference
Multi-armed_bandit
{\displaystyle p} vertices. It can also be maintained dynamically in sublinear time per update. The relative convex hull of a finite set of points is
Relative_convex_hull
Algorithms to generate prime numbers
include sieving using the methods from the Sieve of Eratosthenes can run in sublinear time complexity of O ( N / log log N ) {\displaystyle O(N/\log \log
Generation_of_primes
Compressed full-text substring index
occurrence. The query time, as well as the required storage space, has a sublinear complexity with respect to the size of the input data. The original authors
FM-index
realignment, rectilinear, rectilinearity, sesquilinear, sublineage, sublinear, supralinear, trilinear, unilinear line- smear, smudge Latin linere delete
List of Greek and Latin roots in English/H–O
List_of_Greek_and_Latin_roots_in_English/H–O
Property of a function
Inner measure Subadditivity – Property of some mathematical functions Sublinear function – Type of function in linear algebra M. Marcus, H. Minc (1992)
Superadditivity
Species of moth
reaching the costa, marked anteriorly with a series of ill-defined black sublinear marks, and on the terminal edge with a series of small brownish spots
Cryptophasa_curialis
Israeli-American computer scientist
algorithms. In the area of mathematical optimization, Hazan proposed the first sublinear-time algorithms for linear classification as well as semi-definite programming
Elad_Hazan
Mathematical expression
nearly 50 terms for five decimals and nearly 120 for six. Both converge sublinearly. On the other hand: π = 4 1 + 1 2 3 + 2 2 5 + 3 2 7 + ⋱ = 4 − 1 + 1 6
Continued_fraction
Normed vector space that is complete
{\displaystyle f:X\to \mathbb {R} } is a subadditive function (such as a norm, a sublinear function, or real linear functional), then f {\displaystyle f} is continuous
Banach_space
Probabilistic inequality applying on sum of bounded random variables
\varepsilon } . Hence, the cost of acquiring the confidence interval is sublinear in terms of confidence level and quadratic in terms of precision. Note
Hoeffding's_inequality
On unit fractions adding to 4/n
number of counterexamples grows only sublinearly. Even more strongly, for any fixed k {\displaystyle k} , only a sublinear number of values of n {\displaystyle
Erdős–Straus_conjecture
Tree containing all suffixes of a given text
{\displaystyle O(m+z)} time. Search for a regular expression P in time expected sublinear in n {\displaystyle n} . Find for each suffix of a pattern P {\displaystyle
Suffix_tree
Computer science problem
2022). Bannai, Hideo; Holub, Jan (eds.). Longest Palindromic Substring in Sublinear Time. Combinatorial Pattern Matching. Leibniz International Proceedings
Longest_palindromic_substring
Graph minor formed from subgraphs of small diameter
hereditary graph family has a separator theorem where the separator size is a sublinear power of n if and only if it has polynomial expansion. Nešetřil & Ossona
Shallow_minor
Species of moth
dots runs to the tornus. There is also a terminal series of dark fuscous sublinear dots. The hindwings are pale whitish ochreous. Wikimedia Commons has media
Gonioterma_bolistis
Mathematical operation on matrices
Liam Roditty and Asaf Shapira. 2008. All-Pairs Shortest Paths with a Sublinear Additive Error. ICALP '08, Part I, LNCS 5125, pp. 622–633, 2008. Floyd–Warshall
Min-plus matrix multiplication
Min-plus_matrix_multiplication
Randomized algorithm
by Jeffrey Vitter that it is possible to obtain faster algorithms with sublinear runtime when the algorithm is allowed to skip past sections of the input
Reservoir_sampling
American computer scientist
security. Rubinfeld has also made important contributions to the study of sublinear-time algorithms, which are algorithms that do not need to process the
Ronitt_Rubinfeld
In applied mathematics, a technique to find the shortest path
ISBN 978-3-662-48971-0. Blum, Johannes; Funke, Stefan; Storandt, Sabine (2018). Sublinear Search Spaces for Shortest Path Planning in Grid and Road Networks (PDF)
Contraction_hierarchies
Technique in numerical linear algebra
ICML'17. arXiv:1705.06730. Bakshi, Ainesh L.; Woodruff, David P. (2018). Sublinear Time Low-Rank Approximation of Distance Matrices. NeurIPS. arXiv:1809
Low-rank_approximation
Hypothetical computing devices
instructions called "input λ0,λ1" and "output β". It is difficult to study sublinear space complexity on multi-tape machines with the traditional model, because
Turing_machine_equivalents
Risk assessment ratio in toxicology
other defenses are more active. Moreover, evidence for thresholds or sublinear responses at low doses (including adaptive and protective effects) means
Margin_of_exposure
Analysis of datasets using techniques from topology
{\displaystyle F,G\colon P\to D} when P {\textstyle P} is equipped with a sublinear projection or superlinear family, in which still remains a pseudometric
Topological_data_analysis
Any planar graph can be subdivided by removing a few vertices
including the wheel graphs and star graphs, have no edge separator with a sublinear number of edges, because any edge separator would have to include all
Planar_separator_theorem
Difference between two successive prime numbers
{\displaystyle g_{n}<p_{n}\varepsilon } Hoheisel (1930) was the first to show a sublinear dependence; that there exists a constant θ < 1 {\displaystyle \theta <1}
Prime_gap
Species of lichen
to 8 cm wide. Its lobes are overlapping like roof tiles (imbricate), sublinear to subirregular (somewhat linear to somewhat irregular) in shape, irregularly
Myelochroa_macrogalbinica
of Boyer–Moore Boyer–Moore string-search algorithm: amortized linear (sublinear in most times) algorithm for substring search Knuth–Morris–Pratt algorithm:
List_of_algorithms
Memory space for a deterministic Turing machine
deterministic Turing machine. Several important space complexity classes are sublinear, that is, smaller than the size of the input. Thus, "charging" the algorithm
DSPACE
Species of lichen-forming fungus
that is morphologically identical to P. sulcata. It is characterised by sublinear lobes with marginal and laminal, elongated pseudocyphellae, and soralia
Parmelia_sulcata
Linear map from a vector space to its field of scalars
1991, Th. 3.2)—If p : X → R {\displaystyle p:X\to \mathbb {R} } is a sublinear function, and f : M → R {\displaystyle f:M\to \mathbb {R} } is a linear
Linear_form
American mathematician (1935–2020)
lengths, one can use tilted squares to leave an uncovered area that is sublinear in the side length of the larger square, unlike the obvious packing with
Ronald_Graham
Optimization algorithm
in the feasible set. The convergence of the Frank–Wolfe algorithm is sublinear in general: the error in the objective function to the optimum is O (
Frank–Wolfe_algorithm
\langle k\rangle =2L/N} in G N {\displaystyle G_{N}} scales linearly or sublinearly with N: G N {\displaystyle G_{N}} is dense if ⟨ k ⟩ = O ( N ) {\displaystyle
Sparse_network
Species of crayfish
areola (a structure which runs along the centre of the cephalothorax) is sublinear, or mostly uncurved. Like other decapods, C. gentryi has ten pairs of
Cambarus_gentryi
shown to approximate the Robinson-Foulds distance with a bounded error in sublinear time. In phylogenetics, the metric is often used to compute a distance
Robinson–Foulds_metric
Species of lichen
paratasmanica is characterised by the loosely adnate thallus, the sublinear to sublinear-elongate lobes, the scattered or effigurate maculae on the upper
Xanthoparmelia_paratasmanica
Numerical analysis series acceleration method
method is applied to a sublinearly converging series and accelerates convergence considerably. The convergence is still sublinear, but much faster than
Aitken's delta-squared process
Aitken's_delta-squared_process
Association for Computing Machinery for contributions to delegated computation, sublinear time algorithms and property testing Rob A. Rutenbar, ACM Fellow, IEEE
List of University of Michigan alumni
List_of_University_of_Michigan_alumni
Scientific field studying cities as complex systems
measures of infrastructure (such as the number of gas stations) scale sublinearly with population size. They argue for a quantitative, predictive framework
Urban_scaling
Species of lichen
(leathery) texture. Its lobes are imbricate (overlapping like roof tiles), sublinear to irregular in shape, and measure 3–5 mm in width. The margins are eciliate
Hypotrachyna_neosingularis
Species of gastropod
whorls, 4 on penultimate whorl, broad and flatly rounded (interstices sublinear) and cutting up axials into blunt laterally-elongate tubercles. A fifth
Alvania_minuta
Canadian computer scientist (1968–2010)
for approximating the weight of the Euclidean minimum spanning tree in sublinear time, and finding a tight integrality gap for the vertex cover problem
Avner_Magen
Element of an ordered vector space
≤ t u } {\displaystyle p(x):=\inf\{t\in \mathbb {R} :x\leq tu\}} is a sublinear functional. Suppose ( X , ≤ ) {\displaystyle (X,\leq )} is an ordered
Order_unit
Topic in computer science
possible. In many cases, the running time of property testing algorithms is sublinear in the instance length. Typically, the goal is first to make the query
Property_testing
Species of moth
irroration runs to the dorsum and there is a curved series of black dots or sublinear marks edged anteriorly with white scales running from the costa before
Neophylarcha
axiality of a given convex shape can be approximated arbitrarily closely in sublinear time, given access to the shape by oracles for finding an extreme point
Axiality_(geometry)
Function with a multiplicative scaling behaviour
always interchangeable. This property is used in the definition of a sublinear function. Minkowski functionals are exactly those non-negative extended
Homogeneous_function
Family of graphs whose shallow minors are sparse graphs
polynomial expansion. Conversely, graphs with polynomial expansion have sublinear separator theorems. Because of the connection between separators and expansion
Bounded_expansion
Species of foliose lichen
width. Its lobes are narrow, ranging from 0.3 to 0.8 mm wide, and have sublinear to elongate forms with subdichotomous to dichotomous branching. The tips
Xanthoparmelia toolbrunupensis
Xanthoparmelia_toolbrunupensis
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