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represented in the natural way by adjacency matrices are solvable in subexponential time simply because the size of the input is the square of the number...

A subexponential distribution may be: A kind of heavy-tailed distribution. A distribution with sufficiently light tails so that a certain Orlicz norm of...

distributions, and the subexponential distributions. In practice, all commonly used heavy-tailed distributions belong to the subexponential class, introduced...

A growth rate is said to be infra-exponential or subexponential if it is dominated by all exponential growth rates, however great the doubling time. A...

in the context of light-tailed distributions, one definition of a subexponential distribution is as a probability distribution whose tails decay at an...

Maier BF, Brockmann D (May 2020). "Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China". Science. 368 (6492):...

NP-complete problems actually have algorithms running in superpolynomial, but subexponential time such as O(2√nn). For example, the independent set and dominating...

satisfiability of 3-CNF Boolean formulas (3-SAT) cannot be solved in subexponential time, 2 o ( n ) {\displaystyle 2^{o(n)}} . More precisely, the usual...

class, sometimes called subexponential distributions, is also useful; note however that the more established meaning of subexponential is almost the opposite...

(LCCs), q-query LCCs are bounded exponentially while LDCs can have subexponential lengths. Classical (algebraic) block codes and convolutional codes are...

Maier BF, Brockmann D (May 2020). "Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China". Science. 368 (6492):...

sieve, on the other hand, manages to search for smooth numbers that are subexponential in the size of n. Since these numbers are smaller, they are more likely...

{\displaystyle c>1} is called subexponential. An algorithm can require time that is both superpolynomial and subexponential; examples of this include the...

independent, zero-mean random variables that are either bounded or subexponential. In the matrix case, the analogous results concern a sum of zero-mean...

transactions. As a scholar, Elgamal published 4 articles: T. ElGamal, "A subexponential-time algorithm for computing discrete logarithms over GF(p2)", IEEE...

) {\displaystyle 2^{O({\sqrt {k}})}n^{O(1)}} , i.e., the problem is subexponential fixed-parameter tractable. This algorithm is again optimal, in the sense...

Chapter 5: Exponential Factoring Algorithms, pp. 191–226. Chapter 6: Subexponential Factoring Algorithms, pp. 227–284. Section 7.4: Elliptic curve method...

Subexponential bound in computational complexity...

Fedor V.; Hajiaghayi, MohammadTaghi; Thilikos, Dimitrios M. (2005), "Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs"...

the function is subexponential of ln n (and superpolynomial). Many general-purpose integer factorization algorithms have subexponential time complexities...

exponential time. That is, there exists an oracle A such that, for all subexponential deterministic-time complexity classes T, the relativized complexity...

computational complexity theory L-notation, used for running times of subexponential algorithms L – A Mathemagical Adventure, a 1984 computer game Android...

has no efficient solution, and in a general black box group lacks a subexponential solution at all. Let G {\displaystyle G} be any group. Denote its group...

fixed parameter tractable, and moreover, is solvable in parameterized subexponential time. The treewidth of G is one less than the number of vertices in...

subgraphs. In 2010, Sanjeev Arora, Boaz Barak and David Steurer found a subexponential time approximation algorithm for the unique games problem. A key ingredient...

diameter of polytopal graphs. It has been proved that all polytopes have subexponential diameter. The recent disproof of the Hirsch conjecture is the first...

F.; Brockmann, Dirk (15 May 2020). "Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China". Science. 368 (6492):...

count all polygonalizations of a set of n {\displaystyle n} points in subexponential time, n O ( n ) {\displaystyle n^{O({\sqrt {n}})}} . Dynamic programming...

{\displaystyle \#(n)} grows more slowly than any exponential function, G has a subexponential growth rate. Any such group is amenable. A free group of finite rank...

teaching students complexity theory. The article "On Superpolylogarithmic Subexponential Functions" by Prof. Alan Sherman writes that Knuth's article was seminal...

{\displaystyle \#(n)} grows more slowly than any exponential function, G has a subexponential growth rate. Any such group is amenable. The ends of a topological space...

{\displaystyle N} . (However, the exponential bound can still be reduced by a subexponential factor on the order of 1 / N {\displaystyle 1/{\sqrt {N}}} ; this follows...

Vorobjov, N. N. Jr. (1988), "Solving systems of polynomial inequalities in subexponential time" (PDF), Journal of Symbolic Computation, 5 (1–2): 37–64, doi:10...

Computational Geometry, one by Gil Kalai in 1992 with a proof of a subexponential upper bound on the diameter of a polytope and another by Samuel Ferguson...

László; Fortnow, Lance; Nisan, Noam; Wigderson, Avi (1993). "BPP has subexponential time simulations unless EXPTIME has publishable proofs". Computational...

meaning there is no family of constant-depth, polynomial (or even subexponential) size circuits using AND, OR, NOT, and MODp gates that can compute a...

that is linear in the number of elements defining the problem, and subexponential in the dimension of the problem. LP-type problems were defined by Sharir...

^{0}} circuit family of subexponential size, many tautologies relating to the pigeonhole principle cannot have subexponential proofs in a proof system...

known groups with intermediate growth (i.e. both superpolynomial and subexponential) are essentially generalizations of Grigorchuk's group, and have faster...

simplex algorithm in linear programming that can be proven to run in subexponential time, for showing that every monotone property of graphs has a sharp...

is a family of linear programs on which the pivoting rule requires subexponentially many iterations to find the optimum. Zadeh's rule belongs to the family...

bound, which was factorial for Seidel's method, could be reduced to subexponential. Welzl's minidisk algorithm has been extended to handle Bregman divergences...

and Stolbunov used ordinary elliptic curves and was found to have a subexponential quantum attack. In March 2014, researchers at the Chinese State Key...

important tool in the construction of approximation algorithms and subexponential-time exact algorithms for NP-complete optimization problems on minor-closed...

Fracturing in Rocks. Springer. Thomas, Mikosch (1999). Regular variation subexponentiality and their applications in probability theory (PDF). eurandom.tue.nl...

2017) A. Brown, D. Fisher, S. Hurtado (2022). "Zimmer's conjecture: Subexponential growth, measure rigidity, and strong property (T)". Annals of Mathematics...

graphs was done by Spielman (1996). For hypergraphs of bounded rank, a subexponential upper bound matching the case of graphs was obtained by Babai & Codenotti...

Benjamin F.; Brockmann, Dirk (2020-05-15). "Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China". Science. 368 (6492):...

takes time O ( b − a ) {\displaystyle O(b-a)} ). For an example of a subexponential time discrete logarithm algorithm, see the index calculus algorithm...

fixed parameter tractable, and moreover, is solvable in parameterized subexponential time. The pathwidth of an interval graph is one less than the size of...

degree of the polynomial. Any low degree PIT problem can be reduced in subexponential time of the size of the circuit to a PIT problem for depth-four circuits;...

and it is known in that case that the Dehn function does not admit a subexponential upper bound. The Dehn functions for SL(m,Z), where m > 4 are quadratic...

of the Blum, Shub & Smale model" 1992 Bernd Gärtner (FU Berlin) "A Subexponential Algorithm for Abstract Optimization Problems" 1991 Anna Gal (Chicago)...

ISBN 978-3-030-96561-7. Maier BF, Brockmann D (2020). "Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China". Science. 368 (6492):...

that such a subexponential time bound is possible for the clique problem in arbitrary graphs, as it would imply similarly subexponential bounds for many...

resolved this long-standing open problem by constructing iO from the subexponential hardness of four well-studied cryptographic assumptions, including LWE...

stating the exponential time hypothesis that 3-SAT cannot be solved in subexponential time in the number of variables, This hypothesis is used to deduce lower...

Although NP-hard, the minimum weight triangulation may be constructed in subexponential time by a dynamic programming algorithm that considers all possible...

approximation scheme, which generalizes to a weighted version of the problem. A subexponential parameterized algorithm for weighted feedback arc sets on tournaments...

Wayback Machine Erschler, Anna (2004). "Boundary behaviour for groups of subexponential growth". Annals of Mathematics. 160 (3): 1183–1210. doi:10.4007/annals...

then f ( f ( x ) ) {\displaystyle f{\bigl (}f(x){\bigr )}} is either subexponential or superexponential. Thus, a Hardy L-function cannot be half-exponential...

Benjamin; Brockmann, Dirk (15 May 2020). "Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China". Science. 368 (6492):...

asserts that the majority function cannot be computed by AC0 circuits of subexponential size. For any x, y, and z, the ternary median operator ⟨x, y, z⟩ satisfies...

existence of groups of intermediate growth. Finitely generated groups of subexponential growth are amenable. A suitable subsequence of balls will provide a...

Gil Kalai for making progress on the Hirsch conjecture by proving subexponential bounds on the diameter of d-dimensional polytopes with n facets. Neil...

Advances in Cryptology – -Proceedings of Crypto, 1983 L. Adleman, A subexponential algorithm for the discrete logarithm problem with applications to cryptography...

problem is hard to approximate. In particular, if NP cannot be solved in subexponential time, then it cannot be approximated to within a factor of n γ {\displaystyle...

Discrete Logarithm Problem (DLP) in a finite field. It has heuristic subexponential complexity. Leonard Adleman developed it in 1994 and then elaborated...

positive semidefinite matrices is NP-hard to approximate within any subexponential factor. If further conditions on the spectrum are imposed, the permanent...

Diffie–Hellman scheme is not secure against nonuniform adversaries working in subexponential time. Alekhnovich and Razborov (2008) proved that tree-like Resolution...

Koblitz, Neal (March 1998). "The Improbability That an Elliptic Curve Has Subexponential Discrete Log Problem under the Menezes—Okamoto—Vanstone Algorithm"....

fixed-parameter tractable algorithm, in time polynomial in the graph size and subexponential in k. The treewidth (minimum clique size of a chordal completion) and...

ISBN 978-3-540-54869-0. Matoušek, Jiří; Sharir, Micha; Welzl, Emo (1996), "A subexponential bound for linear programming" (PDF), Algorithmica, 16 (4–5): 498–516...

an independence oracle, it is impossible to find the girth using a subexponential number of matroid queries. Similarly, for a real linear matroid of rank...

6 Suppose a complete algorithm A {\displaystyle {\mathcal {A}}} has subexponential time bound T and a partial algorithm B {\displaystyle {\mathcal {B}}}...

Kim, Eun Jung; Rzazewski, Pawel; Sikora, Florian (2018), "QPTAS and subexponential algorithm for maximum clique on disk graphs", in Speckmann, Bettina;...

3-colorings of string graphs, when they exist, can be found in the subexponential time bound 2 O ( n 2 / 3 log ⁡ n ) {\displaystyle 2^{O(n^{2/3}\log n)}}...

searching over separators strategy to solve some NP-Hard problems in subexponential time", Algorithmica, 9 (4): 398–423, doi:10.1007/bf01228511, S2CID 2722869...

2307/3597283. JSTOR 3597283. S2CID 7965653. Kuperberg, Greg (2005). "A subexponential-time quantum algorithm for the dihedral hidden subgroup problem". SIAM...

for computing a Kemeny ranking, and there also exists a parameterized subexponential-time algorithm with running time O*(2O(√OPT)) for computing such a ranking...

general. It is NP-hard to approximate permanents of PSD matrices within a subexponential factor, and it is conjectured to be BPP NP {\displaystyle {\textsf {BPP}}^{\textsf...

29 (1993), no. 1, pp. 1-13. Vyacheslav S. Krushkal and Frank Quinn, "Subexponential groups in 4-manifold topology." Geometry & Topology 4 (2000), pp. 407–430...

are more efficient than generic discrete logarithm solvers or even subexponential. Hence these hyperelliptic curves must be avoided. Considering various...

O ~ ( n 2 ) {\displaystyle {\tilde {O}}(n^{2})} -Ideal-SVP against subexponential quantum attacks. It achieves asymptotically optimal efficiency: the...

Battarbee, C.; Kahrobaei, D.; Perret, L.; Shahandashti, S. F. (2024). "A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem". Post-Quantum...

Maier BF, Brockmann D (May 2020). "Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China". Science. 368 (6492):...

in the case of a non-enzymatic template replication that leads to a subexponential or a parabolic growth. This could be observed during the stages preceding...

for resolution proofs of dense random 3-satisfiability instances, and subexponential upper bounds for the same dense random instances using the Davis–Putnam...

Sergei (1994), "Factorization of polynomials over finite fields in subexponential time under GRH", Algorithmic Number Theory, Lecture Notes in Computer...

Sergei (1994), "Factorization of polynomials over finite fields in subexponential time under GRH", Algorithmic Number Theory, Lecture Notes in Computer...

"Independent Set, Induced Matching, and Pricing: Connections and Tight (Subexponential Time) Approximation Hardnesses". 2013 IEEE 54th Annual Symposium on...

Björklund, Henrik; Vorobyov, Sergei (2007-01-15). "A combinatorial strongly subexponential strategy improvement algorithm for mean payoff games". Discrete Applied...