Balanced number partitioning is a variant of multiway number partitioning in which there are constraints on the number of items allocated to each set. The input to the problem is a set of n items of different sizes, and two integers m, k. The output is a partition of the items into m subsets, such that the number of items in each subset is at most k. Subject to this, it is required that the sums of sizes in the m subsets are as similar as possible. An example application is identical-machines scheduling where each machine has a job-queue that can hold at most k jobs. The problem has applications also in manufacturing of VLSI chips, and in assigning tools to machines in flexible manufacturing systems. In the standard three-field notation for optimal job scheduling problems, the problem of minimizing the largest sum is sometimes denoted by "P | # ≤ k | Cmax". The middle field "# ≤ k" denotes that the number of jobs in each machine should be at most k. This is in contrast to the unconstrained version, which is denoted by "". (Wikipedia).
A brief introduction to partitions and combinatorics. This video is part of the #MegaFavNumbers project. More videos can be found here: https://www.youtube.com/playlist?list=PLar4u0v66vIodqt3KSZPsYyuULD5meoAo
From playlist MegaFavNumbers
Ex 5: Division Involving Mixed Numbers - Compare Alternative and Traditional Methods
This video explains an alternative method that can be used to divide mixed numbers. The method involving obtaining a common denominator and then dividing the numerators. The video shows the alternative method and the traditional method of multiplying by the reciprocal.
From playlist Multiplying and Dividing Mixed Numbers
This video is about Dividing Mixed Numbers
From playlist Fractions and Decimals
Ex 2: Determine Factors of a Number
This is the second of three videos that provides examples of how to determine the factors of a number using a numbers prime factors. Search Video Library at http://www.mathispower4u.wordpress.com
From playlist Factors and Prime Factorization
This video explains how to divide a decimal by a whole number and how to divide a decimal by a decimal. http://mathispower4u.wordpress.com/
From playlist Number Sense - Decimals, Percents, and Ratios
Ex5: Division Involving Mixed Numbers - Compare Alternative and Traditional Methods
This video explains an alternative method that can be used to divide mixed numbers. The method involving obtaining a common denominator and then dividing the numerators. The video shows the alternative method and the traditional method of multiplying by the reciprocal. Site: http://mathi
From playlist Multiplying and Dividing Fractions
Partial Quotients - Dividing Whole Numbers
The video explains how to use the method of partial quotients to divide whole numbers. This is an alternative method to performing long division. Library: http://www.mathispower4u.com Search: http://www.mathispower4u.wordpress.com
From playlist Multiplication and Division of Whole Numbers
Multiplying and Dividing Mixed Numbers
This video explains how to multiply and divide mixed numbers. http://mathispower4u.yolasite.com/
From playlist Multiplying and Dividing Mixed Numbers
Lecture 7. Graph partitioning algorithms.
Network Science 2021 @ HSE http://www.leonidzhukov.net/hse/2021/networks/
From playlist Network Science, 2021
Steffen Borgwardt: The role of partition polytopes in data analysis
The field of optimization, and polyhedral theory in particular, provides a powerful point of view on common tasks in data analysis. In this talk, we highlight the role of the so-called partition polytopes and their studies in clustering and classification. The geometric properties of parti
From playlist Workshop: Tropical geometry and the geometry of linear programming
Ilse Fischer: The alternating sign matrices/descending plane partitions relation: n+3 pairs of...
CIRM HYBRID EVENT Recorded during the meeting "Lattice Paths, Combinatorics and Interactions" the June 25, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians
From playlist Combinatorics
Corinna Ulcigrai - 3/4 Chaotic Properties of Area Preserving Flows
Flows on surfaces are one of the fundamental examples of dynamical systems, studied since Poincaré; area preserving flows arise from many physical and mathematical examples, such as the Novikov model of electrons in a metal, unfolding of billiards in polygons, pseudo-periodic topology. In
From playlist Corinna Ulcigrai - Chaotic Properties of Area Preserving Flows
Network Science. Lecture11.Graph partitioning algorithms
Graph partitioning algorithms Lecture slides: http://www.leonidzhukov.net/hse/2020/networks/lectures/lecture11.pdf
From playlist Network Science. Module 2, 2020
CS50W 2018 - Lecture 10 - Scalability
TABLE OF CONTENTS 00:00:00 - Introduction 00:03:29 - Benchmarking 00:04:22 - Vertical Scaling 00:06:08 - Horizontal Scaling 00:09:42 - Load Balancing Methods 00:14:43 - Session-Aware Load Balancing 00:19:40 - Autoscaling 00:35:20 - Scaling Databases 00:38:00 - Database Partitioning 00:48:
From playlist CS50's Web Programming with Python and JavaScript
Algorithms - Searching & Data Structures - Lecture 4
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.coderi
From playlist ArsDigita Algorithms by Shai Simonson
This video introduces signed graphs and signed graph theory. Signed graphs are graphs where the edges are given a positive or negative sign. They see applications in scheduling (signed graph coloring specifically), data science, social psychology, and more. In future videos we'll look at c
From playlist Summer of Math Exposition Youtube Videos
Ex 1: Multiplying Signed Mixed Number
This video provides two examples of multiplying signed mixed numbers. Search Video Library at http://www.mathispower4u.wordpress.com
From playlist Multiplying and Dividing Mixed Numbers
Proving super-polynomial lower bounds for syntactic multilinear branching programs by Ramya C
Discussion Meeting Workshop on Algebraic Complexity Theory  ORGANIZERS Prahladh Harsha, Ramprasad Saptharishi and Srikanth Srinivasan DATE & TIME 25 March 2019 to 29 March 2019 VENUE Madhava Lecture Hall, ICTS Bangalore Algebraic complexity aims at understanding the computationa
From playlist Workshop on Algebraic Complexity Theory 2019
Proof: Regular Bipartite Graph is Balanced | Graph Theory, Partite Sets
If G is an r-regular bipartite graph, r greater than 0, with partite sets U and W, then |U| = |W|, that is, the number of vertices in both partite sets is the same! Such a bipartite graph - one with partite sets of equal cardinalities - is called balanced. We will prove this result in toda
From playlist Graph Theory
This video explains how to perform division using whole numbers. http://mathispower4u.yolasite.com/
From playlist Multiplying and Dividing Whole Numbers