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16. Complexity: P, NP, NP-completeness, Reductions
 
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MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Erik Demaine In this lecture, Professor Demaine introduces NP-completeness. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 87826 MIT OpenCourseWare
R8. NP-Complete Problems
 
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MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Amartya Shankha Biswas In this recitation, problems related to NP-Completeness are discussed. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 42988 MIT OpenCourseWare
P vs. NP and the Computational Complexity Zoo
 
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Hackerdashery #2 Inspired by the Complexity Zoo wiki: https://complexityzoo.uwaterloo.ca/Complexity_Zoo For more advanced reading, I highly recommend Scott Aaronson's blog, Shtetl-Optimized: http://www.scottaaronson.com/blog/ ----- Retro-fabulous, cabinet-sized computers: System/360: http://en.wikipedia.org/wiki/IBM_System/360 photo: "360-91-panel". Licensed under Public domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:360-91-panel.jpg#mediaviewer/File:360-91-panel.jpg PDP-8: http://en.wikipedia.org/wiki/PDP-8 photo: "PDP-8". Licensed under Public domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:PDP-8.jpg#mediaviewer/File:PDP-8.jpg ----- Protein folding illustration: "Protein folding schematic" by Tomixdf (talk) - Own work (Original text: “self-made”). Licensed under Public domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:Protein_folding_schematic.png#mediaviewer/File:Protein_folding_schematic.png P vs. NP opinion poll: http://www.cs.umd.edu/~gasarch/papers/poll2012.pdf
Views: 1563632 hackerdashery
17. Complexity: Approximation Algorithms
 
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MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Srinivas Devadas In this lecture, Professor Devadas introduces approximation algorithms in the context of NP-hard problems. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 19672 MIT OpenCourseWare
18. Complexity: Fixed-Parameter Algorithms
 
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MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Erik Demaine In this lecture, Professor Demaine tackles NP-hard problems using fixed-parameter algorithms. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 13364 MIT OpenCourseWare
Factoring Is Still Hard - Applied Cryptography
 
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This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.
Views: 6043 Udacity
20. Asynchronous Distributed Algorithms: Shortest-Paths Spanning Trees
 
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MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Nancy Ann Lynch In this lecture, Professor Lynch introduces asynchronous distributed algorithms. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 5398 MIT OpenCourseWare
R5. Dynamic Programming
 
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MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Ling Ren In this recitation, problems related to dynamic programming are discussed. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 42161 MIT OpenCourseWare
19. Synchronous Distributed Algorithms: Symmetry-Breaking. Shortest-Paths Spanning Trees
 
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MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Nancy Ann Lynch In this lecture, Professor Lynch introduces synchronous distributed algorithms. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 9086 MIT OpenCourseWare
Introduction to Approximation Algorithms - K Center Problem
 
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We introduce the topic of approximation algorithms by going over the K-Center Problem
Views: 17401 CSBreakdown
Approximation Algorithms
 
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Subject:Computer Science Paper: Design and analysis of algorithms
Views: 236 Vidya-mitra
R9. Approximation Algorithms: Traveling Salesman Problem
 
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MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Amartya Shankha Biswas In this recitation, problems related to approximation algorithms are discussed, namely the traveling salesman problem. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 42251 MIT OpenCourseWare
Accepting Certificate - Intro to Algorithms
 
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This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
Views: 415 Udacity
A Tutorial on the Likely Worst-Case Complexities of NP-Complete Problems - Russell Impagliazzo
 
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Russell Impagliazzo Institute for Advanced Study January 24, 2012 Abstract The P vs. NP problem has sometimes been unofficially paraphrased as asking whether it is possible to improve on exhaustive search for such problems as Satisfiability, Clique, Graph Coloring, etc. However, known algorithms for each of these problems indeed are substantially better than exhaustive search, if still exponential. Furthermore, although a polynomial-time algorithm for any one of these problems implies one for all of them, these improved exponential algorithms are highly specific, and it is unclear what the limit of improvement should be. In the past 15 years or so, a complexity theory for exponential complexities has emerged. Fundamental to this theory are two related hypotheses: the Exponential Time Hypothesis, that each k-SAT problem requires time 2ckn for 0 Time Hypothesis, that these constants tend towards 1 as k grows. Like the Unique Games Conjecture for approximation algorithms, there is no consensus on whether these hypotheses are true or false. However, also like UGC, there are many consequences both of their truth and of their falsity. Either way gives a unified picture of the complexities of many NP-complete problems. Furthermore, recent work has shown that ETH and SETH have implications beyond exponential time algorithms, to parameterized complexity, cryptography, data structures, and to the question of whether fundamental polynomial-time algorithms can be further improved. In this talk, I will discuss these hypotheses and their implications for complexity. We’ll see how they can be used to get results about which problems in NP might require exponential time, give evidence that some NP-complete problems are strictly harder than others, and characterize the hard instances of NP-complete problems. We’ll touch on recent work by Williams giving relationships between improved algorithms and circuit lower bounds. We’ll show how to translate results from the exponential realm to reason that certain polynomial time algorithms are unlikely to be improveable. This is a survey of many results, only a fraction of which I am involved with, so I won’t give a complete list of references. However, my work on this subject is joint with Ramamohan Paturi and our students, Francis Zane, Chris Calabro and William Matthews. For more videos, visit http://video.ias.edu
Scaling a solution of an NP-hard problem with Apache ZooKeeper (Kyrylo Holodnov, Ukraine)
 
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NP-hard problems play an important role in cryptography and are frequent in graph theory. Large number of computers don’t reduce a complexity of an algorithm, but a solid architecture and design of distributed system can provide good scalability. In this talk, I will solve a non-standard NP-hard problem and will give examples how to solve it in a cluster of machines using Apache ZooKeeper.
Views: 547 jeeconf
Algorithms || P vs NP || Part - 1
 
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This is a brief video series on P vs NP problem. Please visit the playlist for more videos
Views: 1198 InnovateHub .in
What is STRONG NP-COMPLETENESS? What does STRONG NP-COMPLETENESS mean?
 
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What is STRONG NP-COMPLETENESS? What does STRONG NP-COMPLETENESS mean? STRONG NP-COMPLETENESS meaning - STRONG NP-COMPLETENESS definition - STRONG NP-COMPLETENESS explanation. Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license. SUBSCRIBE to our Google Earth flights channel - https://www.youtube.com/channel/UC6UuCPh7GrXznZi0Hz2YQnQ In computational complexity, strong NP-completeness is a property of computational problems that is a special case of NP-completeness. A general computational problem may have numerical parameters. For example, the input to the bin packing problem is a list of objects of specific sizes and a size for the bins that must contain the objects—these object sizes and bin size are numerical parameters. A problem is said to be strongly NP-complete (NP-complete in the strong sense), if it remains so even when all of its numerical parameters are bounded by a polynomial in the length of the input. A problem is said to be strongly NP-hard if a strongly NP-complete problem has a polynomial reduction to it; in combinatorial optimization, particularly, the phrase "strongly NP-hard" is reserved for problems that are not known to have a polynomial reduction to another strongly NP-complete problem. Normally numerical parameters to a problem are given in positional notation, so a problem of input size n might contain parameters whose size is exponential in n. If we redefine the problem to have the parameters given in unary notation, then the parameters must be bounded by the input size. Thus strong NP-completeness or NP-hardness may also be defined as the NP-completeness or NP-hardness of this unary version of the problem. For example, bin packing is strongly NP-complete while the 0-1 Knapsack problem is only weakly NP-complete. Thus the version of bin packing where the object and bin sizes are integers bounded by a polynomial remains NP-complete, while the corresponding version of the Knapsack problem can be solved in pseudo-polynomial time by dynamic programming. While weakly NP-complete problems may admit efficient solutions in practice as long as their inputs are of relatively small magnitude, strongly NP-complete problems do not admit efficient solutions in these cases. From a theoretical perspective any strongly NP-hard optimization problem with a polynomially bounded objective function cannot have a fully polynomial-time approximation scheme (or FPTAS) unless P = NP. However, the converse fails: e.g. if P does not equal NP, knapsack with two constraints is not strongly NP-hard, but has no FPTAS even when the optimal objective is polynomially bounded. Some strongly NP-complete problems may still be easy to solve on average, but it's more likely that difficult instances will be encountered in practice.
Views: 92 The Audiopedia
Understanding the Empirical Hardness of NP-Complete Problems I
 
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Kevin Leyton-Brown, University of British Columbia https://simons.berkeley.edu/talks/kevin-leyton-brown-08-25-2016-1 Algorithms and Uncertainty Boot Camp
Views: 859 Simons Institute
11. Dynamic Programming: All-Pairs Shortest Paths
 
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MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Erik Demaine In this lecture, Professor Demaine covers different algorithmic solutions for the All-Pairs Shortest Paths problem. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 34320 MIT OpenCourseWare
P vs. NP by Sammy Mehra
 
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Introduction to the most famous unsolved problem in Computer Science. Introduction to Turing Machines, runtime of algorithms, and the classes P and NP. What would the universe look like if P=NP. History of the problem, and attempts to solve the problem. Example adapted from https://en.wikipedia.org/wiki/Reduction_(complexity).
Views: 13885 CS50
8. Randomization: Universal & Perfect Hashing
 
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MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Erik Demaine In this lecture, Professor Demaine reviews hashing in the context of randomized algorithms. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 23576 MIT OpenCourseWare
R11. Cryptography: More Primitives
 
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MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Ling Ren In this recitation, problems related to cryptography are discussed. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 3371 MIT OpenCourseWare
P=NP? - Intro to Algorithms
 
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This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
Views: 1083 Udacity
!!Con 2016 - My favorite NP-complete problem! By Mark Dominus
 
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My favorite NP-complete problem! By Mark Dominus NP-complete problems are the hardest problems whose solutions can be efficiently checked for correctness. An efficient method of solving any NP-complete problem would translate directly into efficient solutions for all of them. Many famous and interesting problems are NP-complete, but this is not one of them! This is the problem of how to distribute “Elmo’s World” segments onto a series of video releases. Nobody knows a good way to solve NP-complete problems. The Elmo’s World people were not able to solve their problem either. Help us caption & translate this video! http://amara.org/v/KLIN/
Views: 1364 Confreaks
R6. Greedy Algorithms
 
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MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Amartya Shankha Biswas In this recitation, problems related to greedy algorithms are discussed. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 24735 MIT OpenCourseWare
22. Cryptography: Encryption
 
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MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Srinivas Devadas In this lecture, Professor Devadas continues with cryptography, introducing encryption methods. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 15420 MIT OpenCourseWare
Gadgets - Intro to Algorithms
 
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This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
Views: 1870 Udacity
What is complexity theory? (P vs. NP explained visually)
 
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A visual explanation of p vs. np and the difference between polynomial vs exponential growth. This marks the end of the CS series! Support new content: https://www.patreon.com/artoftheproblem
Views: 29529 Art of the Problem
What is HAMILTONIAN COMPLETION? What does HAMILTONIAN COMPLETION mean?
 
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What is HAMILTONIAN COMPLETION? What does HAMILTONIAN COMPLETION mean? HAMILTONIAN COMPLETION meaning - HAMILTONIAN COMPLETION definition - HAMILTONIAN COMPLETION explanation. Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license. SUBSCRIBE to our Google Earth flights channel - https://www.youtube.com/channel/UC6UuCPh7GrXznZi0Hz2YQnQ The Hamiltonian completion problem is to find the minimal number of edges to add to a graph to make it Hamiltonian. The problem is clearly NP-hard in general case (since its solution gives an answer to the NP-complete problem of determining whether a given graph has a Hamiltonian cycle). The associated decision problem of determining whether K edges can be added to a given graph to produce a Hamiltonian graph is NP-complete. Moreover, Hamiltonian completion belongs to the APX complexity class, i.e., it is unlikely that efficient constant ratio approximation algorithms exist for this problem. The problem may be solved in polynomial time for certain classes of graphs, including series-parallel graphs and their generalizations, which include outerplanar graphs, as well as for a line graph of a tree or a cactus graph. Gamarnik et al. use a linear time algorithm for solving the problem on trees to study the asymptotic number of edges that must be added for sparse random graphs to make them Hamiltonian.
Views: 52 The Audiopedia
Solving sudoku to beat cancer: P vs NP
 
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My submission for the 2018 Breakthrough Junior Challenge 🐣 Credits - Technical Assistance: Raag Sethi Gifs: Giphy Music: Dust by M.O.O.N #breakthroughjuniorchallenge
Views: 120 Samarth Jajoo
From RSA to P vs. NP the Trailer!
 
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for the part that mentions: “links in the description:” https://www.youtube.com/watch?v=YX40hbAHx3s Sources also listed in video: References [1] Pomerance, Carl, Selfridge, and Samuel Wagstaff, Jr. "The Pseudoprimes." Mathematics of Computation 35.151 (1980): 1094-024. American Mathematical Society. Web. [2] "Baillie–PSW Primality Test." Wikipedia. Wikimedia Foundation, 31 Mar. 2017. Web. 07 Apr. 2017. [3] Nicely, Thomas R. "The Baillie-PSW Primality Test." Trnicely.net. N.p., 10 June 2005. Web. [4] Wolfram Alpha [5] https://wiki.python.org/moin/TimeComplexity [6] https://ivokoller.com/rsa-part-3/ Media Sources Cormac. "Boston Irish." October 2012. N.p., 25 Oct. 2012. Web. 23 Apr. 2017. Schnickledooger. "Schnickledooger." Someone Please Help the Skywalker Family. N.p., 02 July 2014. Web. 23 Apr. 2017. "New Books." Introduction to Cryptography. N.p., n.d. Web. 23 Apr. 2017. Pinterest "Night Photos." Free Stock Photos. N.p., n.d. Web. 23 Apr. 2017. http://l4wisdom.com/python/python_list.php http://stackoverflow.com/questions/111307/whats-p-np-and-why-is-it-such-a-famous-question http://demonstrations.wolfram.com/Pseudoprime/ https://en.wikipedia.org/wiki/Binary_search_algorithm#/media/File:Binary_Search_Depiction.svg Python images - https://www.youtube.com/watch?v=HfzCpDilEVM https://en.wikipedia.org/wiki/Lucas–Lehmer_primality_test https://ivokoller.com/rsa-part-3/ https://www.businesscomputingworld.co.uk/5-things-your-files-would-tell-you-if-they-could-talk/ oh no face - http://wazzuptonight.com/never-lose-car-again/oh-no1/ https://en.wikipedia.org/wiki/RSA_(cryptosystem) The trump - https://www.youtube.com/watch?v=EEA33bAXyNM background Music : https://www.youtube.com/watch?v=L5oNESifgpk https://www.youtube.com/watch?v=tUgUqlm9nzo
Views: 168 evlynn hofbauer
13. Incremental Improvement: Max Flow, Min Cut
 
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MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Srinivas Devadas In this lecture, Professor Devadas introduces network flow, and the Max Flow, Min Cut algorithm. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 42111 MIT OpenCourseWare
23. Cache-Oblivious Algorithms: Medians & Matrices
 
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MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Erik Demaine In this lecture, Professor Demaine introduces cache-oblivious algorithms. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 8003 MIT OpenCourseWare
Jean-Francois Biasse: A polynomial time quantum algorithm for computing class groups
 
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"This paper presents a polynomial time quantum algorithms for computing the ideal class group and solving the principal ideal problem (PIP) in arbitrary classes of number fields under the Generalized Riemann Hypothesis. Previously, these problems were known to have polynomial time solutions in classes of fixed degree number fields by a result of Hallgren [Hallgren'STOC05]. Our new algorithm relies on the recent quantum polynomial time algorithm for solving the Hidden Subgroup Problem of Eistentrager et al. [EHKS STOC14]. Computing the class group and solving the PIP are fundamental problems in number theory. In particular, they are connected to many unproven conjectures in both analytic and algebraic number theory. Our algorithms also directly apply to the computation of relative class groups and unit groups, to the computation of ray class groups and to the the resolution of norm equations. Moreover, the resolution of the PIP is a key component in the cryptanalysis of cryptosystems based on the hardness of finding a short generator in a principal ideal."
Views: 363 Microsoft Research
Randomized Algorithm - Introduction to  Algorithm - Analysis of Algorithm
 
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Randomized Algorithm Video Lecture from Introduction to Algorithm Chapter of Analysis of Algorithm for Computer Engineering Sudent Watch Previous Videos of Introduction to Algorithm Chapter :- 1) Insertion Sort - Introduction to Algorithm - Analysis of Algorithm - https://youtu.be/Y5zjusdoUdg 2) Analysis of Selection Sort and Insertion Sort - Introduction to Algorithm - Analysis of Algorithm - https://youtu.be/RLkQbDdy40o Watch Next Videos of Introduction to Algorithm Chapter :- 1) Recursion Algorithm - Introduction to Algorithm - Analysis of Algorithm - https://youtu.be/0_7d0ynkgHw Access the Complete Playlist of Introduction to Algorithm Chapter :- http://gg.gg/Introduction-to-Algorithm-AOA Access the Complete Playlist of Analysis of Algorithm Subject :- http://gg.gg/Analysis-of-Algorithms-AOA Subscribe to Ekeeda Channel to access more videos :- http://gg.gg/Subscribe-Now #IntroductiontoAlgorithm #AnalysisofAlgorithm #AnalysisofAlgorithmVideoLecture #AnalysisofAlgorithmTutorial #OnlineVideoLectures #EkeedaOnlineLectures #EkeedaVideoLectures #EkeedaVideoTutorial #EkeedaComputerEngineering Thanks For Watching. You can follow and Like us on following social media. Website - http://ekeeda.com Parent Channel - https://www.youtube.com/c/ekeeda Facebook - https://www.facebook.com/ekeeda Twitter - https://twitter.com/Ekeeda_Video LinkedIn- https://www.linkedin.com/company-beta... Instgram - https://www.instagram.com/ekeeda_/ Pinterest - https://in.pinterest.com/ekeedavideo You can reach us on [email protected] Happy Learning : )
Views: 4476 Ekeeda
6. Randomization: Matrix Multiply, Quicksort
 
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MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Srinivas Devadas In this lecture, Professor Devadas introduces randomized algorithms, looking at solving sorting problems with this new tool. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 18499 MIT OpenCourseWare
Complexity classes of algorithms
 
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Innopolis University BS3-1
Views: 451 Nikita Borodulin
Simon's Algorithm
 
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Overview of Chapter 18, Simon's Algorithm, in "A Course in Quantum Computing" (by Michael Loceff)
Views: 2360 michael loceff
Polynomial vs. Pseudo-Polynomial
 
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Debunking the subtle differences between the two very similar program runtimes, and highlighting why this distinction is so important.
Views: 7363 CSBreakdown
P vs. NP - An Introduction
 
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P vs. NP is one of the greatest unsolved problems. Just what is it, and why is it so important? Created by: Cory Chang Produced by: Vivian Liu Script Editor: Justin Chen, Brandon Chen, Elaine Chang, Zachary Greenberg Twitter: https://twitter.com/UBehavior — Extra Resources: hackerdashery’s video: https://youtu.be/YX40hbAHx3s Wiki: https://en.wikipedia.org/wiki/P_versus_NP_problem Cook-Levin Theorem: https://en.wikipedia.org/wiki/Cook–Levin_theorem SAT: https://en.wikipedia.org/wiki/Boolean_satisfiability_problem P: https://en.wikipedia.org/wiki/P_(complexity) NP: https://en.wikipedia.org/wiki/NP_(complexity) EXPTIME: https://en.wikipedia.org/wiki/EXPTIME NP-complete problems: https://en.wikipedia.org/wiki/List_of_NP-complete_problems Picture Credits: https://commons.wikimedia.org/wiki/File%3APyruvate_kinase_protein_domains.png: By Thomas Splettstoesser (www.scistyle.com) (Own work) [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons https://cdn.vox-cdn.com/thumbor/PGO0kRZpyvRAFfhdAAJ73-w9e98=/0x25:680x408/1600x900/cdn.vox-cdn.com/uploads/chorus_image/image/42598430/deep-blue-kasparov.0.jpeg
Views: 61956 Undefined Behavior
Luca Trevisan: Average-case Complexity -- A Survey
 
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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-case complexity of computational problems. We will talk about questions such as: - Can we derive the existence of hard-on-average problems from the existence of hard-in-worst-case problems? What is stopping us from proving statements like "Unless P=NP, there are hard-on-average problems in NP under the uniform distribution" or "Unless P=NP, public-key cryptography is possible"? - What is going on in Levin's famously concise one-page paper on average-case NP-complete problems? - For some, but not all, optimization problems, the hardest instances to approximate are random ones. What does this have to do with integrality gaps and inapproximability results?
Randomised Computation
 
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Randomised Computation, by Daria Dicu Abstract: Randomised algorithms are the simplest and fastest known solution to many decision problems. We reason about randomised algorithms using the concept of probabilistic Turing machines, which are a variant of nondeterministic Turing machines that have probabilistic transition choice. This talk is aimed as a discussion around the various complexity classes associated with randomised computation (BPP, RP, ZPP ). I shall start by presenting these classes, alongside known relationships between them and complexity classes studied in the Part IB course (P, NP). We will then see how randomised algorithms provide much more efficient solutions than deterministic ones by looking at the Schwartz-Zippel lemma applied to Polynomial Identity Testing, which gives a polynomial time Monte Carlo algorithm, as opposed to its deterministic counterpart, which is exponential. In conclusion, I shall discuss the open problem of P = BPP and the usage of pseudorandom number generators to deterministically simulate randomised algorithms.
Fang Song: Zero-knowledge proof systems for QMA
 
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"Prior work has established that all problems in NP admit classical zero-knowledge proof systems, and under reasonable hardness assumptions for quantum computations, these proof systems can be made secure against quantum attacks. We prove a result representing a further quantum generalization of this fact, which is that every problem in the complexity class QMA has a quantum zero-knowledge proof system. More specifically, assuming the existence of an unconditionally binding and quantum computationally concealing commitment scheme, we prove that every problem in the complexity class QMA has a quantum interactive proof system that is zero-knowledge with respect to efficient quantum computations. Our QMA proof system is sound against arbitrary quantum provers, but only requires an honest prover to perform polynomial-time quantum computations, provided that it holds a quantum witness for a given instance of the QMA problem under consideration. The proof system relies on a new variant of the QMA-complete local Hamiltonian problem in which the local terms are described by Clifford operations and standard basis measurements. We believe that the QMA-completeness of this problem may have other uses in quantum complexity."
Views: 531 Microsoft Research
Scott Aaronson - Fundamental Limits of Quantum Computing
 
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Scott Aaronson, a former IQC postdoctoral fellow, talks about his research interests at MIT - quantum computing and computational complexity theory. He's working to discover the limits of the quantum computer, citing np complete problems as an example. Find out more about IQC! Website - https://uwaterloo.ca/institute-for-quantum-computing/ Facebook - https://www.facebook.com/QuantumIQC Twitter - https://twitter.com/QuantumIQC
What is DETERMINISTIC ALGORITHM? What does DETERMINISTIC ALGORITHM mean?
 
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What is DETERMINISTIC ALGORITHM? What does DETERMINISTIC ALGORITHM mean? DETERMINISTIC ALGORITHM meaning - DETERMINISTIC ALGORITHM definition - DETERMINISTIC ALGORITHM explanation. Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license. SUBSCRIBE to our Google Earth flights channel - https://www.youtube.com/channel/UC6UuCPh7GrXznZi0Hz2YQnQ In computer science, a deterministic algorithm is an algorithm which, given a particular input, will always produce the same output, with the underlying machine always passing through the same sequence of states. Deterministic algorithms are by far the most studied and familiar kind of algorithm, as well as one of the most practical, since they can be run on real machines efficiently. Formally, a deterministic algorithm computes a mathematical function; a function has a unique value for any input in its domain, and the algorithm is a process that produces this particular value as output. Deterministic algorithms can be defined in terms of a state machine: a state describes what a machine is doing at a particular instant in time. State machines pass in a discrete manner from one state to another. Just after we enter the input, the machine is in its initial state or start state. If the machine is deterministic, this means that from this point onwards, its current state determines what its next state will be; its course through the set of states is predetermined. Note that a machine can be deterministic and still never stop or finish, and therefore fail to deliver a result. Examples of particular abstract machines which are deterministic include the deterministic Turing machine and deterministic finite automaton. A variety of factors can cause an algorithm to behave in a way which is not deterministic, or non-deterministic: If it uses external state other than the input, such as user input, a global variable, a hardware timer value, a random value, or stored disk data. If it operates in a way that is timing-sensitive, for example if it has multiple processors writing to the same data at the same time. In this case, the precise order in which each processor writes its data will affect the result. If a hardware error causes its state to change in an unexpected way. Although real programs are rarely purely deterministic, it is easier for humans as well as other programs to reason about programs that are. For this reason, most programming languages and especially functional programming languages make an effort to prevent the above events from happening except under controlled conditions. The prevalence of multi-core processors has resulted in a surge of interest in determinism in parallel programming and challenges of non-determinism have been well documented. A number of tools to help deal with the challenges have been proposed to deal with deadlocks and race conditions. It is advantageous, in some cases, for a program to exhibit nondeterministic behavior. The behavior of a card shuffling program used in a game of blackjack, for example, should not be predictable by players — even if the source code of the program is visible. The use of a pseudorandom number generator is often not sufficient to ensure that players are unable to predict the outcome of a shuffle. A clever gambler might guess precisely the numbers the generator will choose and so determine the entire contents of the deck ahead of time, allowing him to cheat; for example, the Software Security Group at Reliable Software Technologies was able to do this for an implementation of Texas Hold 'em Poker that is distributed by ASF Software, Inc, allowing them to consistently predict the outcome of hands ahead of time. These problems can be avoided, in part, through the use of a cryptographically secure pseudo-random number generator, but it is still necessary for an unpredictable random seed to be used to initialize the generator. For this purpose a source of nondeterminism is required, such as that provided by a hardware random number generator. Note that a negative answer to the P=NP problem would not imply that programs with nondeterministic output are theoretically more powerful than those with deterministic output. The complexity class NP (complexity) can be defined without any reference to nondeterminism using the verifier-based definition.
Views: 1491 The Audiopedia
5. Amortization: Amortized Analysis
 
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MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Erik Demaine In this lecture, Professor Demaine introduces analysis techniques for data structures, and the implementation of algorithms based on this analysis. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 36120 MIT OpenCourseWare

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