Reduction (complexity)

Polynomial-time reduction

In computational complexity theory, a polynomial-time reduction is a method for solving one problem using another. One shows that if a hypothetical subroutine solving the second problem exists, then the first problem can be solved by transforming or reducing it to inputs for the second problem and calling the subroutine one or more times. If both the time required to transform the first problem to the second, and the number of times the subroutine is called is polynomial, then the first problem is polynomial-time reducible to the second. A polynomial-time reduction proves that the first problem is no more difficult than the second one, because whenever an efficient algorithm exists for the second problem, one exists for the first problem as well. By contraposition, if no efficient algorithm exists for the first problem, none exists for the second either. Polynomial-time reductions are frequently used in complexity theory for defining both complexity classes and complete problems for those classes. (Wikipedia).

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Reduction of Order - Linear Second Order Homogeneous Differential Equations Part 1

This video explains how to apply the method of reduction of order to solve a linear second order homogeneous differential equations. Site: http://mathispower4u

From playlist Second Order Differential Equations: Reduction of Order

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Solve a System of Equations Using Elimination with Fractions

👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e

From playlist Solve a System of Equations Using Elimination | Hard

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Reduction of Order - Linear Second Order Homogeneous Differential Equations Part 2

This video explains how to apply the method of reduction of order to solve a linear second order homogeneous differential equations. Site: http://mathispower4u

From playlist Second Order Differential Equations: Reduction of Order

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Graphing a System of Equations by Eliminating the Fractions

👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e

From playlist Solve a System of Equations Using Elimination | Hard

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Solve a System of Linear Equations Using Elimination

👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e

From playlist Solve a System of Equations Using Elimination | Hard

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Solve a System of Equations with Elimination when Your Solutions are Fractions

👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e

From playlist Solve a System of Equations Using Elimination | Hard

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NP Completeness II & Reductions - Lecture 16

All rights reserved for http://www.aduni.org/ Published under the Creative Commons Attribution-ShareAlike license http://creativecommons.org/licenses/by-sa/2.0/ Tutorials by Instructor: Shai Simonson. http://www.stonehill.edu/compsci/shai.htm Visit the forum at: http://www.coderisland.c

From playlist ArsDigita Algorithms by Shai Simonson

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Solving a system of equations with infinite many solutions

👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e

From playlist Solve a System of Equations Using Elimination | Medium

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On some fine-grained questions in algorithms and complexity – V. Vassilevska Williams – ICM2018

Mathematical Aspects of Computer Science Invited Lecture 14.8 On some fine-grained questions in algorithms and complexity Virginia Vassilevska Williams Abstract: In recent years, a new “fine-grained” theory of computational hardness has been developed, based on “fine-grained reductions”

From playlist Mathematical Aspects of Computer Science

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Rasmus Kyng: Two-Commodity Flow is as Hard as Linear Programming

We give a nearly-linear time reduction that encodes any linear program polynomially bounded coefficients and solution as a 2-commodityflow problem with only a polylogarithmic blow-up in size. Our reduction applies to high-accuracy approximation algorithms and exact algorithms. Our reductio

From playlist Workshop: Approximation and Relaxation

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CTNT 2020 - Semistable models of hyperelliptic curves over residue characteristic 2 - Jeffrey Yelton

The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2020 - Conference Videos

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Complexity Theory, Quantified Boolean Formula

Theory of Computation 15. Complexity Theory, Quantified Boolean Formula ADUni

From playlist [Shai Simonson]Theory of Computation

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(Ex 2.1B2): Find a General Solution to a 2nd Order Linear Homogenous DE (Reduction of Order)

This video explains how to perform reduction of order to solve a second order linear homogeneous differential equation. https://mathispower4u.com

From playlist Differential Equations: Complete Set of Course Videos

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15. NP-Completeness

MIT 18.404J Theory of Computation, Fall 2020 Instructor: Michael Sipser View the complete course: https://ocw.mit.edu/18-404JF20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY Quickly reviewed last lecture. Covered NP-completeness; SAT and 3SAT;

From playlist MIT 18.404J Theory of Computation, Fall 2020

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NP Completeness III - More Reductions - Lecutre 17

All rights reserved for http://www.aduni.org/ Published under the Creative Commons Attribution-ShareAlike license http://creativecommons.org/licenses/by-sa/2.0/ Tutorials by Instructor: Shai Simonson. http://www.stonehill.edu/compsci/shai.htm Visit the forum at: http://www.coderisland.c

From playlist ArsDigita Algorithms by Shai Simonson

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20. L and NL, NL = coNL

MIT 18.404J Theory of Computation, Fall 2020 Instructor: Michael Sipser View the complete course: https://ocw.mit.edu/18-404JF20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY Reviewed log space: NL is a subset of SPACE(log^2n) and NL is a subse

From playlist MIT 18.404J Theory of Computation, Fall 2020

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Richard Lassaigne: Introduction à la théorie de la complexité

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Mathematical Aspects of Computer Science

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Solve a System of Linear Equations Using Elimination

👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e

From playlist Solve a System of Equations Using Elimination | Medium

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Solve a System of Linear Equations Using Elimination

👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e

From playlist Solve a System of Equations Using Elimination | Medium

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Lecture 23: Computational Complexity

MIT 6.006 Introduction to Algorithms, Fall 2011 View the complete course: http://ocw.mit.edu/6-006F11 Instructor: Erik Demaine License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.006 Introduction to Algorithms, Fall 2011

Related pages

NL (complexity) | Karp's 21 NP-complete problems | Decision problem | Complexity class | GI (complexity) | Existential theory of the reals | Polynomial | Contraposition | PSPACE | Formal language | Turing reduction | Many-one reduction | NC (complexity) | P-complete | L (complexity) | Polynomial hierarchy | Truth-table reduction | Truth table | PSPACE-complete | NP (complexity) | Log-space reduction | Graph isomorphism problem | Computational complexity theory | P (complexity) | Reduction (complexity) | Algorithm | AM (complexity) | Crossing number (graph theory) | EXPTIME