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...her=U.S. National Institute of Standards and Technology|work=Dictionary of Algorithms and Data Structures|accessdate=2010-01-10}}</ref> ...e [[quasi-polynomial time]].<ref>{{ComplexityZoo|Class QP: Quasipolynomial-Time|Q#qp}}</ref> ...

{{distinguish|Quasi-polynomial time}} ...bits required to represent it), which is the case for [[polynomial time]] algorithms.<ref>[[Michael R. Garey]] and [[David S. Johnson]]. [[Computers and Intract ...

In [[computer science]] (particularly [[algorithmics]]), a '''polynomial-time approximation scheme''' ('''PTAS''') is a type of [[approximation algorithm ...} being the length of the shortest tour.<ref>[[Sanjeev Arora]], Polynomial-time Approximation Schemes for Euclidean TSP and other Geometric Problems, Journ ...

== Algorithms == R. Krishman and B. Raghavachari (2001) have a [[quasi-polynomial time]] approximation algorithm to solve the problem for directed graphs.<ref nam ...

{{unsolved|mathematics|Can unknots be recognized in polynomial time?}} ...unresolved challenge is to determine if the problem admits a [[polynomial time]] algorithm; that is, whether the problem lies in the complexity class [[P ...

The term "algebraic equation" dates from the time when the main problem of [[algebra]] was to solve [[univariate]] polynomial ...ical analysis|numerical approximations]] to the roots using [[root-finding algorithms]], such as [[Newton's method]]. ...

...exity of a [[computational problem|problem]] is the complexity of the best algorithms that allow solving the problem. ...known algorithms. Therefore, there is a large overlap between analysis of algorithms and complexity theory. ...

==Algorithms and implementations== ...The Pentium III RNG}}</ref> These numbers, however, were only 32 bit, at a time when export controls were on 56 bits and higher, so they were not state of ...

{{Short description|Estimate of time taken for running an algorithm}} {{Redirect-distinguish|Running time|Running Time (film)}} ...

| title=On the Structure of Polynomial Time Reducibility ...problems that require [[quasi-polynomial time]], and can be solved in that time, including finding a large disjoint set of [[unit disk]]s from a given set ...

A '''fully polynomial-time approximation scheme (FPTAS)''' is an [[algorithm]] for finding approximate ...rast to a general [[polynomial-time approximation scheme]] (PTAS). The run-time of a general PTAS is polynomial in the problem size for each specific ε, bu ...

...> since <math>G</math> is minimal in <math>\mathcal{C}</math>. At the same time, <math>G</math> must have a minor in <math>S</math>, since otherwise <math> ==Polynomial time recognition== ...

...rongly related to Galois fields because of which the encoding and decoding algorithms for cyclic codes are computationally efficient. Here <math>i</math> is ''time'' index, <math>j</math> is ''frequency'' and '''<math>V</math>''' is the '' ...

...ttps://www.quantamagazine.org/algorithm-solves-graph-isomorphism-in-record-time-20151214/ |access-date=2023-03-06}}</ref> ...fly retracted the quasi-polynomiality claim and stated a [[sub-exponential time]] complexity bound instead. He restored the original claim five days later. ...

...Chicago]]. His research focuses on [[computational complexity theory]], [[algorithms]], [[combinatorics]], and [[finite groups]], with an emphasis on the intera | title = Monte-Carlo algorithms in graph isomorphism testing ...

...sizes in these systems implies run-time lower bounds on the corresponding algorithms. This connects proof complexity to more applied areas such as [[SAT solver| ...at ''x'' is a ''P''-proof of ''A''. ''P'' is required to run in polynomial time, and moreover, it must hold that ''A'' has a ''P''-proof if and only if ''A ...

.../link.springer.com/10.1007/978-3-319-16721-3 |title=Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebr ...variate polynomial]]s (this is not used in practice since one knows better algorithms). ...

...e the computation of the determinant of the Sylvester matrix with standard algorithms requires <math>O((d+e)^3)</math> arithmetic operations. ...ing determinants. This needs <math>O(n^3)</math> arithmetic operations. As algorithms are known with a better complexity (see below), this method is not used in ...

...röbner bases|Gröbner basis#S-polynomial|the stable polynomials in discrete-time systems|Stable polynomial}} *{{cite book |last=Sturmfels |first=Bernd | title=Algorithms in Invariant Theory | publisher=Springer | year=1993 | isbn=978-0-387-82445 ...

...h), the maximum clique has bounded size and may be found exactly in linear time;<ref>{{harvtxt|Chiba|Nishizeki|1985}}.</ref> however, for the same classes === Exact algorithms === ...