Combinatorics | NP-complete problems
Set packing is a classical NP-complete problem in computational complexity theory and combinatorics, and was one of Karp's 21 NP-complete problems.Suppose one has a finite set S and a list of subsets of S. Then, the set packing problem asks if some k subsets in the list are pairwise disjoint (in other words, no two of them share an element). More formally, given a universe and a family of subsets of ,a packing is a subfamily of sets such that all sets in are pairwise disjoint. The size of the packing is . In the set packing decision problem, the input is a pair and an integer ; the question is whetherthere is a set packing of size or more. In the set packing optimization problem, the input is a pair , and the task is to find a set packing that uses the most sets. The problem is clearly in NP since, given k subsets, we can easily verify that they are pairwise disjoint in polynomial time. The optimization version of the problem, maximum set packing, asks for the maximum number of pairwise disjoint sets in the list. It is a maximization problem that can be formulated naturally as an integer linear program, belonging to the class of packing problems. (Wikipedia).
Introduction to sets || Set theory Overview - Part 1
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
Introduction to Sets and Set Notation
This video defines a set, special sets, and set notation.
From playlist Sets (Discrete Math)
SET is an awesome game that really gets your brain working. Play it! Read more about SET here: http://theothermath.com/index.php/2020/03/27/set/
From playlist Games and puzzles
Introduction to sets || Set theory Overview - Part 2
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
Set Theory (Part 3): Ordered Pairs and Cartesian Products
Please feel free to leave comments/questions on the video and practice problems below! In this video, I cover the Kuratowski definition of ordered pairs in terms of sets. This will allow us to speak of relations and functions in terms of sets as the basic mathematical objects and will ser
From playlist Set Theory by Mathoma
How to Identify the Elements of a Set | Set Theory
Sets contain elements, and sometimes those elements are sets, intervals, ordered pairs or sequences, or a slew of other objects! When a set is written in roster form, its elements are separated by commas, but some elements may have commas of their own, making it a little difficult at times
From playlist Set Theory
What is the Roster Method? (Roster Form) | Set Theory, Writing Sets, Expressing Sets
The roster method is one of several set notations you can use to write a set. It is perhaps the easiest understand, but is only useful for writing out sets when they are finite and small in size, or if they are dictated by an easy to describe pattern (that is finite or infinite). If you ar
From playlist Set Theory
Set Theory (Part 2): ZFC Axioms
Please feel free to leave comments/questions on the video and practice problems below! In this video, I introduce some common axioms in set theory using the Zermelo-Fraenkel w/ choice (ZFC) system. Five out of nine ZFC axioms are covered and the remaining four will be introduced in their
From playlist Set Theory by Mathoma
Set Theory (Part 1): Notation and Operations
Please feel free to leave comments/questions on the video and practice problems below! In this video series, we'll explore the basics of set theory. I assume no experience with set theory in the video series and anyone who's "been around town" in math should understand the videos. To make
From playlist Set Theory by Mathoma
Diophantine analysis in thin orbits - Alex Kontorovich
Special Seminar Topic: Diophantine analysis in thin orbits Speaker: Alex Kontorovich Affiliation: Rutgers University; von Neumann Fellow, School of Mathematics Date: December 8, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Ghostbusters - Invent with Scratch 2.0
Many more games in the free Scratch Programming Playground book! https://inventwithscratch.com/book A ghostbusters game written in Scratch. This screencast tutorial covers all the steps to making this game.
From playlist Scratch Programming
Angular 4 Project Setup with Webpack
A complete tutorial on setting up a highly scalable and configurable Angular 4 project with Webpack. Learn how to optimize your web development throughput with this project configuration! ⭐ Video Outline ⭐ ⌨ Intro: 0:00 ⌨ Project Setup (Boiler Plate), and an intro to TypeScript: 0:32
From playlist Tutorials
Error-Correcting Codes - Swastik Kopparty
Swastik Kopparty Institute for Advanced Study March 23, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Geometry and arithmetic of sphere packings - Alex Kontorovich
Members' Seminar Topic: Geometry and arithmetic of sphere packings Speaker: A nearly optimal lower bound on the approximate degree of AC00 Speaker:Alex Kontorovich Affiliation: Rutgers University Date: October 23, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Introduction Sphere Packing problems by Abhinav Kumar
DISCUSSION MEETING SPHERE PACKING ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the
From playlist Sphere Packing - 2019
Vanessa Robins (11/28/17): Persistence diagrams of bead packings
Uncovering grain-scale mechanisms that underlie the disorder-order transition in assemblies of granular materials is a fundamental problem with technological relevance. To date, the study of granular crystallization has mainly focussed on the symmetry of crystalline patterns while their em
From playlist AATRN 2017
Apollonian packings and the quintessential thin group - Elena Fuchs
Speaker: Elena Fuchs (UIUC) Title: Apollonian packings and the quintessential thin group Abstract: In this talk we introduce the Apollonian group, sometimes coined the “quintessential” thin group, which is the underlying symmetry group of Apollonian circle packings. We review some of the e
From playlist My Collaborators
DjangoCon US 2016 - Confident Asset Deployments With Webpack & Django by Scott Burns
Confident Asset Deployments With Webpack & Django by Scott Burns Webpack What is it? What does it do? Source transformations Output Why Djangos collectstatic is not up to the job? Must run after deployment Doesn't do all the things Slow Integration on both sides Webpack bundle tracker
From playlist DjangoCon US 2016
Tkinter Python Tutorial 2023 | Modern GUI Design With Tkinter | Basics of Tkinter | Simplilearn
🔥Artificial Intelligence Engineer Program (Discount Coupon: YTBE15): https://www.simplilearn.com/masters-in-artificial-intelligence?utm_campaign=TkinterPythonTutorial-PfZaJbZPYXs&utm_medium=Descriptionff&utm_source=youtube 🔥Professional Certificate Program In AI And Machine Learning: https
Determine Sets Given Using Set Notation (Ex 2)
This video provides examples to describing a set given the set notation of a set.
From playlist Sets (Discrete Math)