Searches , social queries for POLYNOMIAL TIME-REDUCTION
Search references for POLYNOMIAL TIME-REDUCTION. Phrases containing POLYNOMIAL TIME-REDUCTION
See searches and references containing POLYNOMIAL TIME-REDUCTION!
Search references for POLYNOMIAL TIME-REDUCTION. Phrases containing POLYNOMIAL TIME-REDUCTION
See searches and references containing POLYNOMIAL TIME-REDUCTION!POLYNOMIAL TIME-REDUCTION
Method for solving one problem using another
In computational complexity theory, a polynomial-time reduction is a method for solving one problem using another. One shows that if a hypothetical subroutine
Polynomial-time_reduction
Complexity class
exists a polynomial-time reduction between any two NP-complete problems; but it indicates where demonstrating this polynomial-time reduction has been
NP-completeness
Complexity class
non-deterministic polynomial-time, there is a polynomial-time reduction from L to H. That is, assuming a solution for H takes 1 unit time, H's solution can
NP-hardness
Problem transformation for counting solutions
computational complexity theory of counting problems, a polynomial-time counting reduction is a type of reduction (a transformation from one problem to another)
Polynomial-time counting reduction
Polynomial-time_counting_reduction
Type of computational algorithm
reductions are also polynomial-time reductions. However, log-space reductions are probably weaker than polynomial-time reductions; while any non-empty, non-full
Log-space_reduction
Computer science concept
within the hierarchy have complete problems (with respect to polynomial-time reductions) that ask if quantified Boolean formulae hold, for formulae with
Polynomial_hierarchy
Measure of algorithmic complexity
computer science, a polynomial-time algorithm is – generally speaking – an algorithm whose running time is upper-bounded by some polynomial function of the
Strongly-polynomial_time
Type of approximation algorithm
In computer science (particularly algorithmics), a polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems
Polynomial-time approximation scheme
Polynomial-time_approximation_scheme
Class in computational complexity theory
P-complete under polynomial-time reductions. If we use NC reductions, that is, reductions that can operate in polylogarithmic time on a parallel computer
P-complete
Logic puzzle
Light Up puzzle is solvable is NP-complete. This is proved by a polynomial-time reduction from Circuit-SAT, which is known to be NP-complete, to Light Up
Light_Up_(puzzle)
Inherent difficulty of computational problems
complexity of reductions, such as polynomial-time reductions or log-space reductions. The most commonly used reduction is a polynomial-time reduction. This means
Computational complexity theory
Computational_complexity_theory
Philosophical view explaining systems in terms of smaller parts
assumes the form of e.g. polynomial-time reduction. Further, in the even more practical domain of software development, reduction can be seen as the inverse
Reductionism
Complexity class
A function computation problem belongs to PPA if it admits a polynomial-time reduction to this graph search problem. A problem is complete for the class
PPA_(complexity)
Complexity class
{P}}\subseteq {\mathsf {FP}}} . Polynomial-time function problems are fundamental in defining polynomial-time reductions, which are used in turn to define
FP_(complexity)
Transformation of one computational problem to another
used (m : many-one reduction, p : polynomial reduction). The mathematical structure generated on a set of problems by the reductions of a particular type
Reduction_(complexity)
Operators to indicate precedence order
symbols Order theory Partially ordered set Directional symbols Polynomial-time reduction Cooley, Brandon. "Ordered Sets" (PDF) (Lecture note for: Introduction
Ordered_set_operators
Technique for reducing number of solutions
show the Valiant–Vazirani theorem: there exists a randomized polynomial-time reduction from the satisfiability problem for Boolean formulas to the problem
Isolation_lemma
Computational problem possibly useful for post-quantum cryptography
version of the shortest vector problem (SVP) in a lattice (a polynomial-time reduction from this SVP problem to the RLWE problem has been presented)
Ring_learning_with_errors
Complexity class
polynomial-time Turing reduction or polynomial-time counting reduction to it. A counting reduction is a pair of polynomial-time transformations from inputs
♯P-complete
Type of Turing reduction
projections where each subsequent reduction notion is weaker than the prior; see polynomial-time reduction and log-space reduction for details. Given decision
Many-one_reduction
Complexity class
if L is in co-NP and for any problem in co-NP, there exists a polynomial-time reduction from that problem to L. Determining if a formula in propositional
Co-NP
Computational property
pseudo-polynomial reduction is more restrictive than the usual poly-time reduction used for NP-hardness proofs. In particular, the pseudo-polynomial reduction
Strong_NP-completeness
Class of problems in computer science
machine in polynomial time with an error probability of less than 1/2 for all instances. The abbreviation PP refers to probabilistic polynomial time. The complexity
PP_(complexity)
Topics referred to by the same term
may refer to: Polynomial-time approximation scheme, an approximation algorithm in computer science Pesetas, Spanish currency PTAS reduction, an approximation-preserving
PTAS
Complexity class
is the set of all function computation problems that admit a polynomial-time reduction to the PIGEON problem, defined as follows: Given a Boolean circuit
PPP_(complexity)
Set of problems in computational complexity theory
can vary based on resource bounds, such as polynomial-time reductions and log-space reductions. Reductions motivate the concept of a problem being hard
Complexity_class
Problem of determining if a Boolean formula could be made true
proving that other problems are also NP-hard. This is done by polynomial-time reduction from 3-SAT to the other problem. An example of a problem where
Boolean satisfiability problem
Boolean_satisfiability_problem
Mathematical construct in computer algebra
a polynomial f is in I, if and only if some/every complete lead-reduction/reduction of f by G produces the zero polynomial; for every S-polynomial s of
Gröbner_basis
Yes/no problem in computer science
this reduction is more liberal than the standard reduction used in computational complexity (sometimes called polynomial-time many-one reduction); for
Decision_problem
Function used in computer cryptography
is computationally equivalent to factoring N (in the sense of polynomial-time reduction). Hence it can be proven that the Rabin collection is one-way
One-way_function
American-Canadian computer scientist, contributor to complexity theory
Proving Procedures", Cook formalized the notions of polynomial-time reduction (also known as Cook reduction) and NP-completeness, and proved the existence
Stephen_Cook
Algorithmic complexity class
and every problem in EXPTIME has a polynomial-time many-one reduction to it. In other words, there is a polynomial-time algorithm that transforms instances
EXPTIME
Algorithm in computational number theory
The Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, Hendrik Lenstra
Lenstra–Lenstra–Lovász lattice basis reduction algorithm
Lenstra–Lenstra–Lovász_lattice_basis_reduction_algorithm
Formal language that can be expressed using a regular expression
and is in fact complete for exponential space with respect to polynomial-time reduction. For a fixed finite alphabet, the theory of the set of all languages
Regular_language
computational number theory. As the reduction of the factorization of multivariate polynomials to that of univariate polynomials does not have any specificity
Factorization of polynomials over finite fields
Factorization_of_polynomials_over_finite_fields
Decision problem in computer science
it exactly. Then, the polynomial time algorithm for approximate subset sum becomes an exact algorithm with running time polynomial in n and 2 P {\displaystyle
Subset_sum_problem
Mathematical problem in cryptography
{\displaystyle q} has to be polynomial in n {\displaystyle n} . Peikert proves that there is a probabilistic polynomial time reduction from the GapSVP ζ , γ
Learning_with_errors
Abstract machine used to study decision problems
in polynomial time, then the oracle machine (with the R {\displaystyle R} -oracle) can solve R ′ {\displaystyle R'} in polynomial time; one can
Oracle_machine
Subset of a graph's vertices, including at least one endpoint of every edge
size at most k {\displaystyle k} ? They are equivalent under polynomial-time reduction by using binary search. The vertex cover problem is an NP-complete
Vertex_cover
Unsolved problem in computer science
the solution to a problem can be verified in polynomial time, must the problem be solvable in polynomial time? More unsolved problems in computer science
P_versus_NP_problem
Polynomial sequence
In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike
Zernike_polynomials
Optimization problem in computer science
that exact SVP in the Euclidean norm is NP-hard under randomized polynomial-time reductions. Subsequent work established randomized hardness of approximation
Lattice_problem
Computational method
mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the
Factorization_of_polynomials
Subfield of computational complexity theory
scale, using fine-grained reductions which show that a polynomial-factor speedup for one problem would yield a polynomial-factor speedup for another
Fine_grained_complexity
Boolean satisfiability is NP-complete and therefore that NP-complete problems exist
used in the current definition of NP-completeness (i.e., by polynomial-time many-one reduction). Cook and Karp each received a Turing Award for this work
Cook–Levin_theorem
Approximation-preserving reduction
reduction to obtain a polynomial-time solution for the problem A. Similarly, our goal in defining PTAS reductions is so that given a PTAS reduction from
PTAS_reduction
Reduction between decision problems that preserves strong NP-completeness
In computational complexity theory, a pseudo-polynomial transformation is a kind of reduction between decision problems that preserves strong NP-completeness
Pseudo-polynomial transformation
Pseudo-polynomial_transformation
Function in algebraic graph theory
The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics. It counts the number of graph colorings as a
Chromatic_polynomial
Algebraic encoding of graph connectivity
The Tutte polynomial, also called the dichromate or the Tutte–Whitney polynomial, is a graph polynomial. It is a polynomial in two variables which plays
Tutte_polynomial
Subfield of mathematical optimization
g. reservoir flow-rates) There is a large amount of literature on polynomial-time algorithms for certain special classes of discrete optimization. A
Combinatorial_optimization
Topics referred to by the same term
assembly Lenstra–Lenstra–Lovász lattice basis reduction algorithm, a polynomial time lattice reduction algorithm Lowest Landau level, wave functions in
LLL
Mathematical operation
reduction problem is defined as finding the basis with the smallest possible defect, then the problem is NP-complete. However, there exist polynomial
Lattice_reduction
Polynomial that permutes a ring
In mathematics, a permutation polynomial (for a given ring) is a polynomial that acts as a permutation of the elements of the ring, i.e. the map x ↦ g
Permutation_polynomial
Algorithm to smooth data points
fitting successive sub-sets of adjacent data points with a low-degree polynomial by the method of linear least squares. When the data points are equally
Savitzky–Golay_filter
Concept in computability theory
Turing reduction in which the oracle machine runs in polynomial time is known as a Cook reduction. The first formal definition of relative computability
Turing_reduction
Algorithm for solving systems of linear equations
In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence
Gaussian_elimination
class NP-easy is the set of function problems that are solvable in polynomial time by a deterministic Turing machine with an oracle for some decision
NP-easy
be solved in quasi-polynomial time in the combined size of its input and output, but whether they can be solved in polynomial time is an open problem
Monotone_dualization
parameter k is said to admit a linear vertex kernel if there is a polynomial time reduction, called a kernelization algorithm, that maps the input instance
Bidimensionality
Unsolved problem in computational complexity theory
in computer science Can the graph isomorphism problem be solved in polynomial time? More unsolved problems in computer science The graph isomorphism problem
Graph_isomorphism_problem
Problem in computer science
problem is also equivalent to set packing – there is a one-to-one polynomial-time reduction between them: Given a set packing problem on a collection S {\displaystyle
Set_packing
Graph with at most one path between any pair of vertices
remains NP-complete. This was proven by Maheshwari (1976) through a polynomial-time reduction from the vertex cover problem. The problem remains NP-complete
Uniconnected_subgraph
cannot run in worst-case polynomial time. There has been extensive research on finding exact algorithms whose running time is exponential with a low
Exact_algorithm
Complexity class
a solution can be calculated in polynomial time and the neighborhood of a solution can be searched in polynomial time. Therefore it is possible to verify
PLS_(complexity)
Algorithm checking for prime numbers
exponential time: the brute force approach would require the expansion of the ( X + a ) n {\displaystyle (X+a)^{n}} polynomial and a reduction mod n {\displaystyle
Agrawal–Kayal–Saxena primality test
Agrawal–Kayal–Saxena_primality_test
NP-complete variant of the Boolean satisfiability problem
x6) ∧ R(x3, x4, x5) Schaefer gives a construction allowing an easy polynomial-time reduction from 3-SAT to one-in-three 3-SAT. Let "(x or y or z)" be a clause
1-in-3-SAT
Computational complexity class
time 2 n O ( 1 ) {\displaystyle 2^{n^{O}(1)}} . By definition, it is contained in NEXPTIME. NE, unlike NEXPTIME, is not closed under polynomial-time many-one
NE_(complexity)
Type of computational problem
polynomial time. Just as NP has NP-complete problems via many-one reductions, #P has #P-complete problems via polynomial-time parsimonious reductions
Counting_problem_(complexity)
Complexity class of approximable problems
general case. The token reconfiguration problem, via L-reduction from set cover. PTAS (polynomial time approximation scheme) consists of problems that can
APX
Standard model in theoretical computer science
complexity theory, arithmetic circuits are the standard model for computing polynomials. Informally, an arithmetic circuit takes as inputs either variables or
Arithmetic_circuit_complexity
Statistics concept
In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable
Polynomial_regression
Mathematical approximation of a function
of a Taylor series is a polynomial of degree n that is called the nth Taylor polynomial of the function. Taylor polynomials are approximations of a function
Taylor_series
bounded halting problem. Theorem 4 There is a notion of generic-polynomial-time reduction with respect to which the distributional bounded halting problem
Generic-case_complexity
Generalization of binary functions
} Different reductions lead to different results. Take for example the following cubic polynomial: f ( x ) = − 2 x 1 + x 2 − x 3 +
Pseudo-Boolean_function
Problem in graph theory
problem may be solved in polynomial time, and this duality allows the maximum cut problem to also be solved in polynomial time for planar graphs. The Maximum-Bisection
Maximum_cut
Combinatorial optimization problem
Fortunately, there are many algorithms for finding the optimal assignment in time polynomial in n. The assignment problem is a special case of the transportation
Assignment_problem
Algorithm in modular arithmetic
use Barrett algorithm for polynomial division, by reversing polynomials and using X-adic arithmetic. Montgomery reduction is another similar algorithm
Barrett_reduction
Notion in computational complexity theory
function. Polynomial-time parsimonious reductions are a special case of a more general class of reductions for counting problems, the polynomial-time counting
Parsimonious_reduction
2^{n^{2}/2}} bound of the LLL reduction. KZ has exponential complexity versus the polynomial complexity of the LLL reduction algorithm, however it may still
Korkine–Zolotarev lattice basis reduction algorithm
Korkine–Zolotarev_lattice_basis_reduction_algorithm
obfuscated) through byte-wise parallelism and space–time tradeoffs. Various CRC standards extend the polynomial division algorithm by specifying an initial shift
Computation of cyclic redundancy checks
Computation_of_cyclic_redundancy_checks
Method of comparing problems by transforming one into another in computability theory
complexity theory is polynomial-time reducibility; a set A is polynomial-time reducible to a set B {\displaystyle B} if there is a polynomial-time function f such
Reduction (computability theory)
Reduction_(computability_theory)
(unambiguous non-deterministic polynomial-time) is the complexity class of decision problems solvable in polynomial time on an unambiguous Turing machine
UP_(complexity)
If there is a polynomial time algorithm for unambiguous-SAT, then NP equals RP
theorem in computational complexity theory stating that if there is a polynomial time algorithm for Unambiguous-SAT, then NP = RP. It was proven by Leslie
Valiant–Vazirani_theorem
Algorithm for transforming one optimization problem into another
approximation-preserving reduction is a pair of functions ( f , g ) {\displaystyle (f,g)} (which often must be computable in polynomial time), such that: f maps
Approximation-preserving reduction
Approximation-preserving_reduction
approximation-preserving reduction. L-reductions in studies of approximability of optimization problems play a similar role to that of polynomial reductions in the studies
L-reduction
18 mathematical problems stated in 1998
Carlos; Pardo, Luis Miguel (2009). "Smale's 17th Problem: Average Polynomial Time to compute affine and projective solutions" (PDF). Journal of the American
Smale's_problems
Algebraic study of differential equations
derivatives, polynomials, and polynomial sets, 2) identifying a polynomial's leading derivative, initial and separant, 3) polynomial reduction, and 4) creating
Differential_algebra
Thesis on the nature of computability
model of computation." The word 'efficiently' here means up to polynomial-time reductions. This thesis was originally called computational complexity-theoretic
Church–Turing_thesis
Algorithm for polynomial evaluation
computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation. It is named after William George Horner, although it is much
Horner's_method
Hypothesis in computational complexity theory
cannot be solved efficiently (where efficiently typically means "in polynomial time"). It is not known how to prove (unconditional) hardness for essentially
Computational hardness assumption
Computational_hardness_assumption
Problem of finding a cycle through all vertices of a graph
The algorithm can check in polynomial time if the vertices in G appear once in c. Additionally, it takes polynomial time to check the start and end vertices
Hamiltonian_path_problem
collisions would be feasible in polynomial time by algorithm A, then one could find and use polynomial time algorithm R (reduction algorithm) that would use
Security of cryptographic hash functions
Security_of_cryptographic_hash_functions
Copy of a directed graph with redundant edges removed
construct, while transitive reductions can be constructed in polynomial time. Transitive reduction can be defined for an abstract binary relation on a set
Transitive_reduction
The polynomial hierarchy is contained in probabilistic Turing machine in polynomial time
problem in the polynomial hierarchy there is a deterministic polynomial-time Turing reduction to a counting problem. An analogous result in the complexity
Toda's_theorem
Complexity class
with associated verification algorithms A1, A2. A reduction P1 and P2 is defined as two polynomial-time computable functions, f and g, such that f maps
FNP_(complexity)
Concepts from linear algebra
the roots of a polynomial with degree 5 or more. (Generality matters because any polynomial with degree n is the characteristic polynomial of some companion
Eigenvalues_and_eigenvectors
Computational hardness assumption
through which it could be attacked. In particular, there exists a polynomial-time reduction from the recognition of small set expanders to the problem of
Small set expansion hypothesis
Small_set_expansion_hypothesis
Network coding concept
r}(a_{i}P_{i})=\sum _{1\leq j\leq r}(b_{j}P_{j}).} Proposition: There is a polynomial time reduction from discrete log on the cyclic group of order p {\displaystyle
Homomorphic signatures for network coding
Homomorphic_signatures_for_network_coding
these languages, but no polynomial time isomorphisms between all such languages and other NP-complete languages are known. Polynomial creativity and the k
Polynomial_creativity
Reconfiguration problem in combinatorics and computational complexity theory
elements (the latter of which is notably a constant). So we have a polynomial-time reduction from set cover, which is NP-complete, to token reconfiguration
Token_reconfiguration
travel, tourism, insurance
POLYNOMIAL TIME-REDUCTION
POLYNOMIAL TIME-REDUCTION
POLYNOMIAL TIME-REDUCTION
POLYNOMIAL TIME-REDUCTION
POLYNOMIAL TIME-REDUCTION
POLYNOMIAL TIME-REDUCTION
POLYNOMIAL TIME-REDUCTION
POLYNOMIAL TIME-REDUCTION
POLYNOMIAL TIME-REDUCTION
travel, tourism, insurance