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P vs. NP and the Computational Complexity Zoo
P vs. NP and the Computational Complexity Zoo -
NP Completeness for dummies: Complexity Classes P and NP (lec 1)
NP Completeness for dummies: Complexity Classes P and NP (lec 1)NP Completeness for dummies: Complexity Classes P and NP (lec 1)
This video lecture is produced by S. Saurabh. He is B.Tech from IIT and MS from USA. NP completeness : classes P and NP To study interview questions on Linked List watch http://www.youtube.com/playlist?list=PL3D11462114F778D7&feature;=view_all To prepare for programming Interview Questions on Binary Trees http://www.youtube.com/playlist?list=PLC3855D81E15BC990&feature;=view_all To study programming Interview questions on Stack, Queues, Arrays visit http://www.youtube.com/playlist?list=PL65BCEDD6788C3F27&feature;=view_all To watch all Programming Interview Questions visit http://www.youtube.com/playlist?list=PLD629C50E1A85BF84&feature;=v -
Computational Complexity
Computational ComplexityComputational Complexity
Spring 2014 @ UVa (advanced undergrad level) Recapping P, NP, coNP and halting theorem Starting: time hierarchy theorem. Course page on Piazza: https://piazza.com/virginia/spring2014/cs45016501/home -
23. Computational Complexity
23. Computational Complexity23. 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 -
Ketan Mulmuley, On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis II
Ketan Mulmuley, On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis IIKetan Mulmuley, On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis II
In this talk Ketan Mulmuley, of IAS, discusses the connection between the P vs NP problem, geometric complexity theory, and the Riemann hypothesis. For references, check out Mulmuley's papers on arxiv: http://arxiv.org/find/cs/1/au:+Mulmuley_K/0/1/0/all/0/1 In particular, check out this one: http://arxiv.org/abs/0908.1936 This talk was given at the School of Mathematics, Institute for Advanced Study at Princeton on February 9, 2009. This talk, as well as many, MANY others can be downloaded at the IAS website -- follow the link below: https://video.ias.edu/csdm/pvsnp/II -
Ketan Mulmuley, On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis I
Ketan Mulmuley, On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis IKetan Mulmuley, On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis I
In this talk Ketan Mulmuley, of IAS, discusses the connection between the P vs NP problem, geometric complexity theory, and the Riemann hypothesis. For references, check out Mulmuley's papers on arxiv: http://arxiv.org/find/cs/1/au:+Mulmuley_K/0/1/0/all/0/1 In particular, check out this one: http://arxiv.org/abs/0908.1936 This talk was given at the School of Mathematics, Institute for Advanced Study at Princeton on February 9, 2009. This talk, as well as many, MANY others can be downloaded at the IAS website -- follow the link below: https://video.ias.edu/csdm/pvsnp/I -
Ketan Mulmuley, On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis III
Ketan Mulmuley, On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis IIIKetan Mulmuley, On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis III
In this talk Ketan Mulmuley, of IAS, discusses the connection between the P vs NP problem, geometric complexity theory, and the Riemann hypothesis. For references, check out Mulmuley's papers on arxiv: http://arxiv.org/find/cs/1/au:+Mulmuley_K/0/1/0/all/0/1 In particular, check out this one: http://arxiv.org/abs/0908.1936 This talk was given at the School of Mathematics, Institute for Advanced Study at Princeton on February 9, 2009. This talk, as well as many, MANY others can be downloaded at the IAS website -- follow the link below: https://video.ias.edu/csdm/pvsnp/III -
Lecture 61/65: Time Complexity Classes P And NP
Lecture 61/65: Time Complexity Classes P And NPLecture 61/65: Time Complexity Classes P And NP
"Theory of Computation"; Portland State University: Prof. Harry Porter; www.cs.pdx/~harry -
Complexity Beyond NP-Hardness: Papadimitriou's New Idea and Its Relation to Complexity of Games
Complexity Beyond NP-Hardness: Papadimitriou's New Idea and Its Relation to Complexity of GamesComplexity Beyond NP-Hardness: Papadimitriou's New Idea and Its Relation to Complexity of Games
Presented by Vladik Kreinvich 3 Apr 2009 at the UTEP CS Colloquium. -
Complexity Classes - The Class NP
Complexity Classes - The Class NPComplexity Classes - The Class NP
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Np vs Complexity Mini
Np vs Complexity MiniNp vs Complexity Mini
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Complexity Classes - NP complete Problems
Complexity Classes - NP complete ProblemsComplexity Classes - NP complete Problems
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Professor Avi Wigderson on the "P vs. NP" problem
Professor Avi Wigderson on the "P vs. NP" problemProfessor Avi Wigderson on the "P vs. NP" problem
Avi Wigderson is a professor of Mathematics at the Institute for Advanced Study in Princeton. After studying Computer Science at Technion in Haifa, he obtain... -
L19: Uncomputable Functions, and Introduction to Complexity
L19: Uncomputable Functions, and Introduction to ComplexityL19: Uncomputable Functions, and Introduction to Complexity
Proof by diagonalization that there are uncomputable functions; introduction to complexity theory, big-Oh notation, definition of worst-case for a non-determ...
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10:44
P vs. NP and the Computational Complexity Zoo
Hackerdashery #2 Inspired by the Complexity Zoo wiki: https://complexityzoo.uwaterloo.ca/C...
published: 26 Aug 2014
author: hackerdashery
P vs. NP and the Computational Complexity Zoo
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P vs. NP and the Computational Complexity Zoo
- published: 26 Aug 2014
- views: 194
- author: hackerdashery
Hackerdashery #2 Inspired by the Complexity Zoo wiki: https://complexityzoo.uwaterloo.ca/Complexity_Zoo For more advanced reading, I highly recommend Scott A...
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8:30
NP Completeness for dummies: Complexity Classes P and NP (lec 1)
This video lecture is produced by S. Saurabh. He is B.Tech from IIT and MS from USA.
NP c...
published: 05 Nov 2014
NP Completeness for dummies: Complexity Classes P and NP (lec 1)
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NP Completeness for dummies: Complexity Classes P and NP (lec 1)
- published: 05 Nov 2014
- views: 9
This video lecture is produced by S. Saurabh. He is B.Tech from IIT and MS from USA. NP completeness : classes P and NP To study interview questions on Linked List watch http://www.youtube.com/playlist?list=PL3D11462114F778D7&feature;=view_all To prepare for programming Interview Questions on Binary Trees http://www.youtube.com/playlist?list=PLC3855D81E15BC990&feature;=view_all To study programming Interview questions on Stack, Queues, Arrays visit http://www.youtube.com/playlist?list=PL65BCEDD6788C3F27&feature;=view_all To watch all Programming Interview Questions visit http://www.youtube.com/playlist?list=PLD629C50E1A85BF84&feature;=view_all To learn about Pointers in C visit http://www.youtube.com/playlist?list=PLC68607ACFA43C084&feature;=view_all To learn C programming from IITian S.Saurabh visit http://www.youtube.com/playlist?list=PL3C47C530C457BACD&feature;=view_all
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83:05
Computational Complexity
Spring 2014 @ UVa (advanced undergrad level)
Recapping P, NP, coNP and halting theorem
Sta...
published: 09 Feb 2014
Computational Complexity
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Computational Complexity
- published: 09 Feb 2014
- views: 14
Spring 2014 @ UVa (advanced undergrad level) Recapping P, NP, coNP and halting theorem Starting: time hierarchy theorem. Course page on Piazza: https://piazza.com/virginia/spring2014/cs45016501/home
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51:12
23. Computational Complexity
MIT 6.006 Introduction to Algorithms, Fall 2011
View the complete course: http://ocw.mit.e...
published: 14 Jan 2013
23. Computational Complexity
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23. Computational Complexity
- published: 14 Jan 2013
- views: 65666
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
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110:47
Ketan Mulmuley, On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis II
In this talk Ketan Mulmuley, of IAS, discusses the connection between the P vs NP problem,...
published: 18 Dec 2014
Ketan Mulmuley, On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis II
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Ketan Mulmuley, On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis II
- published: 18 Dec 2014
- views: 0
In this talk Ketan Mulmuley, of IAS, discusses the connection between the P vs NP problem, geometric complexity theory, and the Riemann hypothesis. For references, check out Mulmuley's papers on arxiv: http://arxiv.org/find/cs/1/au:+Mulmuley_K/0/1/0/all/0/1 In particular, check out this one: http://arxiv.org/abs/0908.1936 This talk was given at the School of Mathematics, Institute for Advanced Study at Princeton on February 9, 2009. This talk, as well as many, MANY others can be downloaded at the IAS website -- follow the link below: https://video.ias.edu/csdm/pvsnp/II
Add to Playlist
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79:13
Ketan Mulmuley, On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis I
In this talk Ketan Mulmuley, of IAS, discusses the connection between the P vs NP problem,...
published: 18 Dec 2014
Ketan Mulmuley, On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis I
add related playlist
Ketan Mulmuley, On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis I
- published: 18 Dec 2014
- views: 0
In this talk Ketan Mulmuley, of IAS, discusses the connection between the P vs NP problem, geometric complexity theory, and the Riemann hypothesis. For references, check out Mulmuley's papers on arxiv: http://arxiv.org/find/cs/1/au:+Mulmuley_K/0/1/0/all/0/1 In particular, check out this one: http://arxiv.org/abs/0908.1936 This talk was given at the School of Mathematics, Institute for Advanced Study at Princeton on February 9, 2009. This talk, as well as many, MANY others can be downloaded at the IAS website -- follow the link below: https://video.ias.edu/csdm/pvsnp/I
Add to Playlist
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120:05
Ketan Mulmuley, On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis III
In this talk Ketan Mulmuley, of IAS, discusses the connection between the P vs NP problem,...
published: 18 Dec 2014
Ketan Mulmuley, On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis III
add related playlist
Ketan Mulmuley, On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis III
- published: 18 Dec 2014
- views: 0
In this talk Ketan Mulmuley, of IAS, discusses the connection between the P vs NP problem, geometric complexity theory, and the Riemann hypothesis. For references, check out Mulmuley's papers on arxiv: http://arxiv.org/find/cs/1/au:+Mulmuley_K/0/1/0/all/0/1 In particular, check out this one: http://arxiv.org/abs/0908.1936 This talk was given at the School of Mathematics, Institute for Advanced Study at Princeton on February 9, 2009. This talk, as well as many, MANY others can be downloaded at the IAS website -- follow the link below: https://video.ias.edu/csdm/pvsnp/III
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12:18
Lecture 61/65: Time Complexity Classes P And NP
"Theory of Computation"; Portland State University: Prof. Harry Porter; www.cs.pdx/~harry...
published: 23 Jan 2015
Lecture 61/65: Time Complexity Classes P And NP
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Lecture 61/65: Time Complexity Classes P And NP
- published: 23 Jan 2015
- views: 3
"Theory of Computation"; Portland State University: Prof. Harry Porter; www.cs.pdx/~harry
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45:07
Complexity Beyond NP-Hardness: Papadimitriou's New Idea and Its Relation to Complexity of Games
Presented by Vladik Kreinvich 3 Apr 2009 at the UTEP CS Colloquium....
published: 09 Nov 2009
author: Eric Freudenthal
Complexity Beyond NP-Hardness: Papadimitriou's New Idea and Its Relation to Complexity of Games
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Complexity Beyond NP-Hardness: Papadimitriou's New Idea and Its Relation to Complexity of Games
- published: 09 Nov 2009
- views: 1394
- author: Eric Freudenthal
Presented by Vladik Kreinvich 3 Apr 2009 at the UTEP CS Colloquium.
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8:33
Complexity Classes - The Class NP
...
published: 04 May 2014
Complexity Classes - The Class NP
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4:18
Np vs Complexity Mini
...
published: 11 Apr 2011
author: TeamNotoriousPK
Np vs Complexity Mini
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Np vs Complexity Mini
- published: 11 Apr 2011
- views: 607
- author: TeamNotoriousPK
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20:40
Complexity Classes - NP complete Problems
...
published: 06 May 2014
author: tudor pc
Complexity Classes - NP complete Problems
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Complexity Classes - NP complete Problems
- published: 06 May 2014
- views: 19
- author: tudor pc
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57:25
Professor Avi Wigderson on the "P vs. NP" problem
Avi Wigderson is a professor of Mathematics at the Institute for Advanced Study in Princet...
published: 14 May 2012
author: ETH Zürich
Professor Avi Wigderson on the "P vs. NP" problem
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Professor Avi Wigderson on the "P vs. NP" problem
- published: 14 May 2012
- views: 17496
- author: ETH Zürich
Avi Wigderson is a professor of Mathematics at the Institute for Advanced Study in Princeton. After studying Computer Science at Technion in Haifa, he obtain...
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81:11
L19: Uncomputable Functions, and Introduction to Complexity
Proof by diagonalization that there are uncomputable functions; introduction to complexity...
published: 13 Dec 2012
author: UCDavis
L19: Uncomputable Functions, and Introduction to Complexity
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L19: Uncomputable Functions, and Introduction to Complexity
- published: 13 Dec 2012
- views: 1920
- author: UCDavis
Proof by diagonalization that there are uncomputable functions; introduction to complexity theory, big-Oh notation, definition of worst-case for a non-determ...
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11:13
P vs. NP
Useful links: Stephen Cook's Introduction to the problem: http://www.claymath.org/millenni...
published: 11 Sep 2010
author: Daniel Page
P vs. NP
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P vs. NP
- published: 11 Sep 2010
- views: 21738
- author: Daniel Page
Useful links: Stephen Cook's Introduction to the problem: http://www.claymath.org/millennium/P_vs_NP/Official_Problem_Description.pdf NP vs. P information: h...
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5:39
NP-hard
NP-hard (Non-deterministic Polynomial-time hard), in computational complexity theory, is a...
published: 30 Aug 2014
author: Audiopedia
NP-hard
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NP-hard
- published: 30 Aug 2014
- author: Audiopedia
NP-hard (Non-deterministic Polynomial-time hard), in computational complexity theory, is a class of problems that are, informally, "at least as hard as the h...
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10:02
The P versus NP Problem (Part 1)
This video is the first in a multi-part series on the P versus NP problem geared for a bro...
published: 16 Mar 2013
author: brainsetmanus
The P versus NP Problem (Part 1)
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The P versus NP Problem (Part 1)
- published: 16 Mar 2013
- views: 27438
- author: brainsetmanus
This video is the first in a multi-part series on the P versus NP problem geared for a broad audience (i.e., one with a very basic understanding of mathemati...
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10:44
The P versus NP Problem (Part 3)
This video is the third in a multi-part series on the P versus NP problem geared for a bro...
published: 16 Mar 2013
author: brainsetmanus
The P versus NP Problem (Part 3)
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The P versus NP Problem (Part 3)
- published: 16 Mar 2013
- views: 4593
- author: brainsetmanus
This video is the third in a multi-part series on the P versus NP problem geared for a broad audience (i.e., one with a very basic understanding of mathemati...
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6:15
More Hiking in Modern Math World (2/7) - Complexity Theory, P versus NP, RSA Cryptography
Learn more on http://www.science4all.org about: P versus NP: http://www.science4all.org/le...
published: 12 Sep 2013
author: Science 4 All
More Hiking in Modern Math World (2/7) - Complexity Theory, P versus NP, RSA Cryptography
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More Hiking in Modern Math World (2/7) - Complexity Theory, P versus NP, RSA Cryptography
- published: 12 Sep 2013
- views: 497
- author: Science 4 All
Learn more on http://www.science4all.org about: P versus NP: http://www.science4all.org/le-nguyen-hoang/pnp/ Divide and Conquer: http://www.science4all.org/l...
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50:08
Introduction to P and NP
Lecture 24 gives an introduction to P and NP and polynomial-time reductions....
published: 01 Oct 2011
author: UCDavis
Introduction to P and NP
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Introduction to P and NP
- published: 01 Oct 2011
- views: 41908
- author: UCDavis
Lecture 24 gives an introduction to P and NP and polynomial-time reductions.
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65:24
Richard Karp: Effective Heuristics for NP-Hard Problems
Richard Karp: Effective Heuristics for NP-Hard Problems In many practical situations heuri...
published: 17 Oct 2011
author: StanfordCSTheory
Richard Karp: Effective Heuristics for NP-Hard Problems
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Richard Karp: Effective Heuristics for NP-Hard Problems
- published: 17 Oct 2011
- views: 1983
- author: StanfordCSTheory
Richard Karp: Effective Heuristics for NP-Hard Problems In many practical situations heuristic algorithms reliably give satisfactory solutions to real-life i...
Richard Karp: Effective Heuristics for NP-Hard Problems
Published: 17 Oct 2011
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9:13
Project Management Agile And Critical Chain P=NP optimization Michael Nir - Voice over
This is an article based on Michael's book: The Agile PMO -- found on Amazon Is NP=P and w...
published: 29 Jan 2014
author: Michael Nir
Project Management Agile And Critical Chain P=NP optimization Michael Nir - Voice over
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Project Management Agile And Critical Chain P=NP optimization Michael Nir - Voice over
- published: 29 Jan 2014
- views: 135
- author: Michael Nir
This is an article based on Michael's book: The Agile PMO -- found on Amazon Is NP=P and why should we really care? Did you notice that when something happen...
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32:47
L20: P, NP and Polynomial-Time Reductions
P, NP, and polynomial-time reductions. Is P = NP?...
published: 13 Dec 2012
author: UCDavis
L20: P, NP and Polynomial-Time Reductions
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L20: P, NP and Polynomial-Time Reductions
- published: 13 Dec 2012
- views: 2727
- author: UCDavis
P, NP, and polynomial-time reductions. Is P = NP?
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61:38
Beyond Computation: The P vs NP Problem - Michael Sipser
Beyond Computation: The P vs NP Problem Michael Sipser, MIT Tuesday, October 3, 2006 at 7:...
published: 23 Nov 2011
author: PoincareDuality
Beyond Computation: The P vs NP Problem - Michael Sipser
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Beyond Computation: The P vs NP Problem - Michael Sipser
- published: 23 Nov 2011
- views: 75008
- author: PoincareDuality
Beyond Computation: The P vs NP Problem Michael Sipser, MIT Tuesday, October 3, 2006 at 7:00 PM Harvard University Science Center — Hall B One Oxford Street,...
Beyond Computation: The P vs NP Problem - Michael Sipser
Published: 23 Nov 2011
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53:06
Luca Trevisan: Average-case Complexity -- A Survey
Luca Trevisan: Average-case Complexity -- A Survey In this survey talk, we review the many...
published: 17 Oct 2011
author: StanfordCSTheory
Luca Trevisan: Average-case Complexity -- A Survey
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Luca Trevisan: Average-case Complexity -- A Survey
- published: 17 Oct 2011
- views: 1017
- author: StanfordCSTheory
Luca Trevisan: Average-case Complexity -- A Survey In this survey talk, we review the many open questions and the few things that are known about the average...
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81:50
NP Completeness II & Reductions - Lecture 16
All rights reserved for http://www.aduni.org/ Published under the Creative Commons Attribu...
published: 31 Oct 2012
author: Coderisland
NP Completeness II & Reductions - Lecture 16
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NP Completeness II & Reductions - Lecture 16
- published: 31 Oct 2012
- views: 11408
- author: Coderisland
All rights reserved for http://www.aduni.org/ Published under the Creative Commons Attribution-ShareAlike license http://creativecommons.org/licenses/by-sa/2...
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29:24
Martin Ziegler: "Computational Complexity of Geometric Quantum Logic"
Speaker: Martin Ziegler (Technical University of Darmstadt) Title: Computational Complexit...
published: 01 May 2012
author: OxfordQuantumVideo
Martin Ziegler: "Computational Complexity of Geometric Quantum Logic"
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Martin Ziegler: "Computational Complexity of Geometric Quantum Logic"
- published: 01 May 2012
- views: 227
- author: OxfordQuantumVideo
Speaker: Martin Ziegler (Technical University of Darmstadt) Title: Computational Complexity of Geometric Quantum Logic Event: Quantum Physics and Logic 2010 ...
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55:12
NP-hardness of Nuclear Norms for Tensors
Shmuel Friedland, University of Illinois at Chicago
Tensors in Computer Science and Geomet...
published: 15 Nov 2014
NP-hardness of Nuclear Norms for Tensors
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NP-hardness of Nuclear Norms for Tensors
- published: 15 Nov 2014
- views: 17
Shmuel Friedland, University of Illinois at Chicago Tensors in Computer Science and Geometry http://simons.berkeley.edu/talks/shmuel-friedland-2014-11-11
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24:47
Topic 24 C NP Complete Problems
Topic 24 C: NP Complete Problems We illustrate the range of NP Complete problems and how t...
published: 09 Dec 2013
author: UHMICSAlgorithms
Topic 24 C NP Complete Problems
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Topic 24 C NP Complete Problems
- published: 09 Dec 2013
- views: 2057
- author: UHMICSAlgorithms
Topic 24 C: NP Complete Problems We illustrate the range of NP Complete problems and how they are shown to be NPC by sketching proofs for several problems in...
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81:50
NP Completeness II & Reductions
Algorithms 16. NP Completeness II & Reductions aduni....
published: 23 Nov 2012
author: Chao Xu
NP Completeness II & Reductions
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NP Completeness II & Reductions
- published: 23 Nov 2012
- views: 3861
- author: Chao Xu
Algorithms 16. NP Completeness II & Reductions aduni.
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58:16
Lecture -26 NP-Completeness-I -Motivation
Lecture Series on Design & Analysis of Algorithms by Prof.Sunder Vishwanathan, Prof.Abhira...
published: 27 Aug 2008
author: nptelhrd
Lecture -26 NP-Completeness-I -Motivation
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Lecture -26 NP-Completeness-I -Motivation
- published: 27 Aug 2008
- views: 36339
- author: nptelhrd
Lecture Series on Design & Analysis of Algorithms by Prof.Sunder Vishwanathan, Prof.Abhiram Ranade, Department of Computer Science Engineering,IIT Bombay. Fo...
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73:51
The History and Status of the P versus NP Question
The History and Status of the P versus NP Question ADUni Speaker: Michael Sipser....
published: 23 Nov 2012
author: Chao Xu
The History and Status of the P versus NP Question
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The History and Status of the P versus NP Question
- published: 23 Nov 2012
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The History and Status of the P versus NP Question ADUni Speaker: Michael Sipser.
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Lecture - 27 NP - Compliteness - II
Lecture Series on Design & Analysis of Algorithms by Prof.Sunder Vishwanathan, Prof.Abhira...
published: 27 Aug 2008
author: nptelhrd
Lecture - 27 NP - Compliteness - II
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Lecture - 27 NP - Compliteness - II
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Lecture Series on Design & Analysis of Algorithms by Prof.Sunder Vishwanathan, Prof.Abhiram Ranade, Department of Computer Science Engineering,IIT Bombay. Fo...
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SAT is NP Complete
SAT is NP Complete...
published: 13 Nov 2014
SAT is NP Complete
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NP Completeness III - More Reductions - Lecutre 17
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published: 31 Oct 2012
author: Coderisland
NP Completeness III - More Reductions - Lecutre 17
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NP Completeness III - More Reductions - Lecutre 17
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The Traveling Salesman Problem and the equality of P and NP Part II
The complexity classes P and NP are equal....
published: 09 Jul 2014
author: Mostafa Tab
The Traveling Salesman Problem and the equality of P and NP Part II
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The Traveling Salesman Problem and the equality of P and NP Part II
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The complexity classes P and NP are equal.
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MIT 6.006 Fall 2011 Lecture 23
Computational complexity: complexity classes (polynomial, exponential, solvable in finite ...
published: 03 Jan 2013
author: Victor Costan
MIT 6.006 Fall 2011 Lecture 23
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MIT 6.006 Fall 2011 Lecture 23
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Computational complexity: complexity classes (polynomial, exponential, solvable in finite time); decision problems; solvable problems; non-deterministic-poly...
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In computational complexity theory, NP is one of the most fundamental complexity classes. The abbreviation NP refers to "nondeterministic polynomial time."
Intuitively, NP is the set of all decision problems for which the instances where the answer is "yes" have efficiently verifiable proofs of the fact that the answer is indeed "yes." More precisely, these proofs have to be verifiable in polynomial time by a deterministic Turing machine. In an equivalent formal definition, NP is the set of decision problems where the "yes"-instances can be decided in polynomial time by a non-deterministic Turing machine. The equivalence of the two definitions follows from the fact that an algorithm on such a non-deterministic machine consists of two phases, the first of which consists of a guess about the solution which is generated in a non-deterministic way, while the second consists of a deterministic algorithm which verifies or rejects the guess as a valid solution to the problem.
The complexity class P is contained in NP, but NP contains many important problems, the hardest of which are called NP-complete problems, for which no polynomial-time algorithms are known for solving them (although they can be verified in polynomial time). The most important open question in complexity theory, the P = NP problem, asks whether polynomial time algorithms actually exist for NP-complete, and by corollary, all NP problems. It is widely believed that this is not the case.
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http://en.wikipedia.org/wiki/NP_(complexity)
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