In computational geometry, a maximum disjoint set (MDS) is a largest set of non-overlapping geometric shapes selected from a given set of candidate shapes. Every set of non-overlapping shapes is an independent set in the intersection graph of the shapes. Therefore, the MDS problem is a special case of the maximum independent set (MIS) problem. Both problems are NP complete, but finding a MDS may be easier than finding a MIS in two respects: * For the general MIS problem, the best known exact algorithms are exponential. In some geometric intersection graphs, there are sub-exponential algorithms for finding a MDS. * The general MIS problem is hard to approximate and doesn't even have a constant-factor approximation. In some geometric intersection graphs, there are polynomial-time approximation schemes (PTAS) for finding a MDS. Finding an MDS is important in applications such as automatic label placement, VLSI circuit design, and cellular frequency division multiplexing. The MDS problem can be generalized by assigning a different weight to each shape and searching for a disjoint set with a maximum total weight. In the following text, MDS(C) denotes the maximum disjoint set in a set C. (Wikipedia).
This video covers the divisibility rules for 2,3,4,5,6,8,9,and 10. http://mathispower4u.yolasite.com/
From playlist Factors, Prime Factors, and Least Common Factors
Ex 1: Apply Divisibility Rules to a 4 Digit Number
This video explains how to apply the divisibility rules for 2, 3, 4, 5, 6, 8, 9, and 10. http://mathispower4u.com
From playlist Factors, Prime Factors, and Least Common Factors
Ex 2: Apply Divisibility Rules to a 4 Digit Number
This video explains how to apply the divisibility rules for 2, 3, 4, 5, 6, 8, 9, and 10. http://mathispower4u.com
From playlist Factors, Prime Factors, and Least Common Factors
#shorts This video reviews the divisibility rule for 3.
From playlist Math Shorts
Ex: The Distributive Property (Mixed Examples)
This video provides several examples of how to apply the distributive property.
From playlist Multiplying Polynomials
From playlist L. Number Theory
Number Theory | Divisibility Basics
We present some basics of divisibility from elementary number theory.
From playlist Divisibility and the Euclidean Algorithm
Divisibility Mathematical Induction Proof: 3 Divides 2^(2n) - 1
In this video I do an induction proof with divisibility. I prove that 3 divides 2^(2n) - 1 for all positive integers n. I hope this video helps someone:)
From playlist Principle of Mathematical Induction
Proof: Menger's Theorem | Graph Theory, Connectivity
We prove Menger's theorem stating that for two nonadjacent vertices u and v, the minimum number of vertices in a u-v separating set is equal to the maximum number of internally disjoint u-v paths. If you want to learn about the theorem, see how it relates to vertex connectivity, and see
From playlist Graph Theory
Intro to Menger's Theorem | Graph Theory, Connectivity
Menger's theorem tells us that for any two nonadjacent vertices, u and v, in a graph G, the minimum number of vertices in a u-v separating set is equal to the maximum number of internally disjoint u-v paths in G. The Proof of Menger's Theorem: https://youtu.be/2rbbq-Mk-YE Remember that
From playlist Graph Theory
Proof: Cosets are Disjoint and Equal Size
Explanation for why cosets of a subgroup are either equal or disjoint and why all cosets have the same size. Group Theory playlist: https://www.youtube.com/playlist?list=PLug5ZIRrShJHDvvls4OtoBHi6cNnTZ6a6 0:00 Cosets are disjoint 3:15 Cosets have same size Subscribe to see more new math
From playlist Group Theory
What are Vertex Disjoint Paths? | Graph Theory
What are vertex disjoint paths in graph theory? Sometimes called pairwise vertex disjoint paths, they're exactly what you'd expect. We say two paths are vertex disjoint if they have no common vertices! We go over some examples, talk about internally disjoint paths, maximum numbers of inter
From playlist Graph Theory
Chandra Chekuri: On element connectivity preserving graph simplification
Chandra Chekuri: On element-connectivity preserving graph simplification The notion of element-connectivity has found several important applications in network design and routing problems. We focus on a reduction step that preserves the element-connectivity due to Hind and Oellerman which
From playlist HIM Lectures 2015
Ahmad Abdi: Packing odd T-joins with at most two terminals
Ahmad Abdi: Packing odd T-joins with at most two terminals Let T be an even vertex subset, of size at most two, and let S be an edge subset of a graph. An edge subset is odd if it contains an odd number of edges of S. We are interested in packing edge-disjoint odd T-joins. The maximum siz
From playlist HIM Lectures 2015
[EXTREME] If He Can Solve This, Help Us Hit 300k Subs!
▶Today's Puzzle◀ Today's puzzle is trailered as being EXTREMELY DIFFICULT! It's by the wonderful constructor Qodec and it's called The Sword. You can play the puzzle here: https://app.crackingthecryptic.com/webapp/f8qbbtF9Lt Rules: Normal sudoku rules apply. Clues outside the grid
From playlist Qodec Puzzles
Topics in Combinatorics lecture 6.9 -- Two applications of the Borsuk-Ulam theorem
Here I show how to use the Borsuk-Ulam theorem to find a graph with no short odd cycles but with very high chromatic number, and then to give a solution to the Kneser conjecture. The latter concerns the chromatic number of the Kneser graph, which has as its vertex set the set of all subset
From playlist Topics in Combinatorics (Cambridge Part III course)
Idealness of k-wise intersecting families, by Tony Huynh
CMSA Combinatorics Seminar, 6 October 2020
From playlist CMSA Combinatorics Seminar
Commutative algebra 14 (Irreducible subsets of Spec R)
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we show that the irreducible closed subsets of Spec R are just the closures of points. We do this using the
From playlist Commutative algebra
The Distributive Law (1 of 2: Using two approaches to subtract fractions & Multiply Fractions)
More resources available at www.misterwootube.com
From playlist Fractions, Decimals and Percentages