The balls into bins (or balanced allocations) problem is a classic problem in probability theory that has many applications in computer science. The problem involves m balls and n boxes (or "bins"). Each time, a single ball is placed into one of the bins. After all balls are in the bins, we look at the number of balls in each bin; we call this number the load on the bin. The problem can be modelled using a Multinomial distribution, and may involve asking a question such as: What is the expected number of bins with a ball in them? Obviously, it is possible to make the load as small as m/n by putting each ball into the least loaded bin. The interesting case is when the bin is selected at random, or at least partially at random. A powerful balls-into-bins paradigm is the "power of two random choices" where each ball chooses two (or more) random bins and is placed in the lesser-loaded bin. This paradigm has found wide practical applications in shared-memory emulations, efficient hashing schemes, randomized load balancing of tasks on servers, and routing of packets within parallel networks and data centers. (Wikipedia).
Thanks to arthritismutilans http://www.youtube.com/user/arthritismutilans and DeeDoubleYou81 http://www.youtube.com/user/DeeDoubleYou81 for the puzzle. If I put my juggling collection into piles of 2 I have one juggling ball left over. If I put my collection into piles of 3 I have 2 l
From playlist My Maths Videos
A Maths Puzzle: Balls, Solution and The Chinese Remainder Theorem
Solution to A Maths Puzzle: Balls, followed by an explanation of the maths behind it. Original video here http://www.youtube.com/watch?v=QmLzX3xn8RE Check out dave597's channel here http://www.youtube.com/user/dave597 and his solution here http://daveman.wordpress.com/2009/07/24/anot
From playlist My Maths Videos
Math for Liberal Studies - Lecture 1.8.1 The Bin-Packing Problem
This is the first video for Math for Liberal Studies Section 1.8: Bin Packing and Scheduling. In this lecture, I discuss the general idea behind the bin-packing problem and talk about several examples of how this problem can occur in the real world.
From playlist Math for Liberal Studies Lectures
Stars and Bars with PIE: Determine the Number of Ways of Putting Balls in Bins with Upper Bound
This video explains how to use the stars and bars method of counting with PIE to solving a counting problem. mathispower4u.com
From playlist Counting (Discrete Math)
Kid Makes Homemade Toy Bowling Alley and Gets A Strike!
Isaac makes a toy bowling alley with two by fours 2 x 4 and gets gutter balls, foul balls and then a strike! Bowling is Fun for Kids!
From playlist Family Videos
Single Hypothesis Learning - Data Science
In this video, we learn that we can learn! We specifically learn that the result of machine learning is simply a summary statistic we can bootstrap and that gives us clues as to why learning works in the first place. Link to my notes on Introduction to Data Science: https://github.com/kna
From playlist Introduction to Data Science - Foundations
Mega millions jackpot probability | Probability and combinatorics | Precalculus | Khan Academy
Probability of winning the Mega Millions jackpot Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/precalculus/prob_comb/prob_combinatorics_precalc/e/probability_with_perm_comb?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus Watch the ne
From playlist High school statistics | High School Math | Khan Academy
Finding Needles in Exponential Haystacks - Joel Spencer
Joel Spencer Courant Institute; NYU February 21, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
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Joel Spencer Courant Institute, NYU February 21, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Visualizing division by fractions
3D animation giving an intuitive understanding of what it means to divide by a fraction.
From playlist Physics
COMBINATIONS with REPETITION - DISCRETE MATHEMATICS
We take a look at combinations with repetition, and discuss integer solution problems. Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--Playlists--* Discrete Mathematics 1: https://www.youtube.com/playlist?list=PLDDGPdw7e6Ag1EIznZ-m-qXu4XX3A0cIz Dis
From playlist Discrete Math 1
Bouncing Balls - Sixty Symbols
Collisions between tiny balls creates a curious effect in this film about the so-called "coefficient of restitution". More physics at http://www.sixtysymbols.com/
From playlist Roger Bowley - Sixty Symbols
Brittany Carr (6/2/20): Zigzag persistence to extract non-linear statistics from optical flow
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From playlist SIAM Topological Image Analysis 2020
The corner cube problem is interesting because it initially looks difficult. When the problem was first posed to me, for example, it didn't know how to solve it. Still, my intuition bells were ringing, telling me there was a nice solution. In this video, I cover two of these solutions, in
From playlist Fun
Approximate nearest neighbor search in high dimensions – Piotr Indyk – ICM2018
Mathematical Aspects of Computer Science Invited Lecture 14.7 Approximate nearest neighbor search in high dimensions Piotr Indyk Abstract: The nearest neighbor problem is defined as follows: Given a set P of n points in some metric space (X,𝖣), build a data structure that, given any poin
From playlist Mathematical Aspects of Computer Science