Complexity classes | Approximation algorithms
In computational complexity theory, the class APX (an abbreviation of "approximable") is the set of NP optimization problems that allow polynomial-time approximation algorithms with approximation ratio bounded by a constant (or constant-factor approximation algorithms for short). In simple terms, problems in this class have efficient algorithms that can find an answer within some fixed multiplicative factor of the optimal answer. An approximation algorithm is called an -approximation algorithm for input size if it can be proven that the solution that the algorithm finds is at most a multiplicative factor of times worse than the optimal solution. Here, is called the approximation ratio. Problems in APX are those with algorithms for which the approximation ratio is a constant . The approximation ratio is conventionally stated greater than 1. In the case of minimization problems, is the found solution's score divided by the optimum solution's score, while for maximization problems the reverse is the case. For maximization problems, where an inferior solution has a smaller score, is sometimes stated as less than 1; in such cases, the reciprocal of is the ratio of the score of the found solution to the score of the optimum solution. A problem is said to have a polynomial-time approximation scheme (PTAS) if for every multiplicative factor of the optimum worse than 1 there is a polynomial-time algorithm to solve the problem to within that factor. Unless P = NP there exist problems that are in APX but without a PTAS, so the class of problems with a PTAS is strictly contained in APX. One such problem is the bin packing problem. (Wikipedia).
From playlist Latest and Greatest
Using Sympy to solve algebraic expressions and equations.
From playlist Introduction to Pyhton for mathematical programming
Visualizing decimal numbers and their arithmetic 67 | Arithmetic and Geometry Math Foundations
This video gives a precise definition of a decimal number as a special kind of rational number; one for which there is an expression a/b where a and b are integers, with b a power of ten. For such a number we can extend the Hindu-Arabic notation for integers by introducing the decimal form
From playlist Math Foundations
Hi-speed video of a golf ball compressed by driver
Recorded at 10,000 fps with the Photron ultima APX slow motion video camera, the gold ball can be seen to compress as the golf club comes ... all » into contact with it at high speed. Recorded with the APX as 10K fps, with a 10 microsecond shutter and 512 (H) x 256 (V) at 10-bit pixel dep
From playlist Impulse
Voyage of Curiosity: A Martian Chronicle 4k
This film tells the epic story of NASA's Curiosity Rover on a mission to find out whether life could ever have existed on Mars and whether the planet is safe for humans. This film tracks the robotic explorer's perilous journey, from its risky landing to its momentous climb up the slopes of
From playlist The Solar System
Extending the capabilities of Python with the Math module
From playlist Introduction to Pyhton for mathematical programming
Tough Circle Geometry Question (2 of 3: Proving a given chord is a diameter)
More resources available at www.misterwootube.com
From playlist Circle Geometry
Biology Quiz: What are organelles?
Ready to make the grade in biology? Subscribe to our new Biology channel to get more quizzes and biology animations! https://bit.ly/3jHu5UP #biology #DNA #shorts
From playlist 1 Minute Biology Quizzes
Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https://twitter.com/worldscienceu
From playlist Science Unplugged: General Relativity
PIR Live Event - Lava Tubes & Missions to Mars
Did you know that Canadian scientists are currently researching in preparation for Mars missions to search for evidence of past life preserved in caves? Dr. Richard Léveillé is one of many scientists preparing for future astrobiology missions to Mars. He is a Participating Scientist at t
From playlist Lava Tubes Playlist
11. Inapproximability Examples
MIT 6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs, Fall 2014 View the complete course: http://ocw.mit.edu/6-890F14 Instructor: Erik Demaine In this lecture, Professor Demaine explains L-reductions to prove various problems APX-complete, introduces a characterization theorem for
From playlist MIT 6.890 Algorithmic Lower Bounds, Fall 2014
Michael Meyer: Mars Exploration Driven by Curiosity
Google Tech Talk December 6, 2012 (expand for more info) Presented by Dr. Michael A. Meyer. ABSTRACT The possibility of life on Mars has become a scientific issue of profound importance, a topic of public interest, and a question that research and space exploration can address. Although
From playlist NASA Speakers at Google
Curiosity Rover Report (Aug. 17, 2012)
Curiosity remains busy on Mars by checking out her instruments and getting ready for her first test drive. Curiosity status reports: www.jpl.nasa.gov/msl
From playlist Curiosity Rover Reports
The St Étienne machine gun of 1907 was developed by the French Government and saw action during WW1. For political reasons,the French did not want to rely on machine guns developed by private firms e.g. Hotchkiss, and by 1905 had developed the Puteaux APX MG. This design avoided, as far
From playlist Automatic Machine Guns
Curiosity Rover Report (Jan. 10, 2013): Giving Mars the Brush-off
NASA's Curiosity rover dusts off a rock on Mars for the first time.
From playlist Curiosity Rover Reports
In this talk, we will define elliptic curves and, more importantly, we will try to motivate why they are central to modern number theory. Elliptic curves are ubiquitous not only in number theory, but also in algebraic geometry, complex analysis, cryptography, physics, and beyond. They were
From playlist An Introduction to the Arithmetic of Elliptic Curves
Curiosity Rover Report (Nov. 29, 2012): Curiosity Roves Again
After spending six weeks doing science investigations at Rocknest, NASA's Curiosity Mars rover is on the move again to Point Lake and a place to try out the drill.
From playlist Curiosity Rover Reports