Number partitioning

Balanced number partitioning

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).

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Partitions (#MegaFavNumbers)

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

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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

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Dividing Mixed Numbers

This video is about Dividing Mixed Numbers

From playlist Fractions and Decimals

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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

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Dividing Decimals

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

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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

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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

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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

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Lecture 7. Graph partitioning algorithms.

Network Science 2021 @ HSE http://www.leonidzhukov.net/hse/2021/networks/

From playlist Network Science, 2021

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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

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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

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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

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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

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CS50W 2018 - Lecture 10 - Scalability

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From playlist CS50's Web Programming with Python and JavaScript

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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

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What are Signed Graphs?

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

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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

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Proving super-polynomial lower bounds for syntactic multilinear branching programs by Ramya C

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From playlist Workshop on Algebraic Complexity Theory 2019

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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

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Dividing Whole Numbers

This video explains how to perform division using whole numbers. http://mathispower4u.yolasite.com/

From playlist Multiplying and Dividing Whole Numbers

Related pages

3-partition problem | Multiway number partitioning | Anytime algorithm | Optimal job scheduling | Multifit algorithm | Identical-machines scheduling | List scheduling | Ordinal data | Matroid-constrained number partitioning | Partition matroid | Uniform matroid | Maximum weight matching | Partition problem | Largest differencing method