Geometric graphs | Spanning tree
A Euclidean minimum spanning tree of a finite set of points in the Euclidean plane or higher-dimensional Euclidean space connects the points by a system of line segments with the points as endpoints, minimizing the total length of the segments. In it, any two points can reach each other along a path through the line segments. It can be found as the minimum spanning tree of a complete graph with the points as vertices and the Euclidean distances between points as edge weights. The edges of the minimum spanning tree meet at angles of at least 60°, at most six to a vertex. In higher dimensions, the number of edges per vertex is bounded by the kissing number of tangent unit spheres. The total length of the edges, for points in a unit square, is at most proportional to the square root of the number of points. Each edge lies in an empty region of the plane, and these regions can be used to prove that the Euclidean minimum spanning tree is a subgraph of other geometric graphs including the relative neighborhood graph and Delaunay triangulation. By constructing the Delaunay triangulation and then applying a graph minimum spanning tree algorithm, the minimum spanning tree of given planar points may be found in time , as expressed in big O notation. This is optimal in some models of computation, although faster randomized algorithms exist for points with integer coordinates. For points in higher dimensions, finding an optimal algorithm remains an open problem. (Wikipedia).
Minimum Spanning Tree In Data Structure | What Is Spanning Tree? | Data Structures|Simplilearn
This video is based on minimum Spanning Trees in Data structures. This Spanning Tree Tutorial will acquaint you with the fundamentals of spanning trees and their importance. It also covers the methodology to generate spanning trees from a given graph. The topics covered in this video are:
From playlist Data Structures & Algorithms [2022 Updated]
From playlist M. Graph Theory
AQA Decision 1 4.01a Introducing Minimum Spanning Trees and Kruskal's Algorithm
I introduce the concept of finding a minimum spanning tree for a network by working through an example of Kruskal's Algorithm.
From playlist [OLD SPEC] TEACHING AQA DECISION 1 (D1)
Discrete Math II - 11.5.1 Minimum Spanning Trees: Prim's Algorithm
A minimum spanning tree finds a spanning tree with a minimum weight. Weights can represent cost of construction, travel time, etc., so finding the least time or cost is of importance to us. In our first algorithm, we explore Prim's Algorithm. In Prim's Algorithm, we search for the least
From playlist Discrete Math II/Combinatorics (entire course)
Prim's Algorithm for Minimum Spanning Trees (MST) | Graph Theory
We go over Prim's Algorithm, and how it works to find minimum spanning trees (also called minimum weight spanning trees or minimum cost spanning trees). We'll also see two examples of using Prim's algorithm to find minimum spanning trees in connected weighted graphs. This algorithm is on
From playlist Graph Theory
Benjamin Schweinhart (4/3/18): Persistent homology and the upper box dimension
We prove the first results relating persistent homology to a classically defined fractal dimension. Several previous studies have demonstrated an empirical relationship between persistent homology and fractal dimension; our results are the first rigorous analogue of those comparisons. Spe
From playlist AATRN 2018
Lecture 18 - Clustering Algorithms
This is Lecture 18 of the CSE549 (Computational Biology) course taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 2010. The lecture slides are available at: http://www.algorithm.cs.sunysb.edu/computationalbiology/pdf/lecture18.pdf More inf
From playlist CSE549 - Computational Biology - 2010 SBU
This is Lecture 14 of the CSE373 (Analysis of Algorithms) course taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 2007. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/video-lectures/2007/lecture13.pdf More informa
From playlist CSE373 - Analysis of Algorithms - 2007 SBU
Lecture 25 - Approximation Algorithms
This is Lecture 25 of the CSE373 (Analysis of Algorithms) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1997. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/video-lectures/1997/lecture26.pdf
From playlist CSE373 - Analysis of Algorithms - 1997 SBU
Kruskal's Algorithm (Decision Maths 1)
Powered by https://www.numerise.com/ Kruskal's Algorithm for finding the minimum spanning tree of a network www.hegartymaths.com http://www.hegartymaths.com/
From playlist Decision Maths 1 OCR Exam Board (A-Level tutorials)
OCR MEI MwA E: Minimum Spanning Trees: 01 Introduction & Greedy Algorithms
https://www.buymeacoffee.com/TLMaths Navigate all of my videos at https://sites.google.com/site/tlmaths314/ Like my Facebook Page: https://www.facebook.com/TLMaths-1943955188961592/ to keep updated Follow me on Instagram here: https://www.instagram.com/tlmaths/ Many, MANY thanks to Dea
From playlist TEACHING OCR MEI Modelling with Algorithms
CSE 373 --- Lecture 14: Shortest Path (Fall 2021)
10/14/21
From playlist CSE373 --- Analysis of Algorithms (Fall 2021)
The Traveling Salesman Problem: When Good Enough Beats Perfect
Use the code "reducible" to get CuriosityStream for less than $15 a year! https://curiositystream.com/reducible The Traveling Salesman Problem (TSP) is one of the most notorious problems in all of computer science. In this video, we dive into why the problem presents such a challenge for
From playlist Graph Theory
Parvaneh Joharinad (7/27/22): Curvature of data
Abstract: How can one determine the curvature of data and how does it help to derive the salient structural features of a data set? After determining the appropriate model to represent data, the next step is to derive the salient structural features of data based on the tools available for
From playlist Applied Geometry for Data Sciences 2022
Discrete Math II - 11.4.1 Spanning Trees - Depth-First Search
We continue our study of trees by examining spanning trees. Spanning trees are subgraphs of a graph that contain all vertices of the original graph. The resulting subgraph is a tree, so the graph is connected and contains no cycles. In our first methodology, we will use a depth-first sear
From playlist Discrete Math II/Combinatorics (entire course)
Lecture 13 - Minimum Spanning Trees I
This is Lecture 13 of the CSE373 (Analysis of Algorithms) course taught by Professor Steven Skiena [http://www3.cs.stonybrook.edu/~skiena/] at Stony Brook University in 2016. The lecture slides are available at: https://www.cs.stonybrook.edu/~skiena/373/newlectures/lecture13.pdf More inf
From playlist CSE373 - Analysis of Algorithms 2016 SBU
CSE373 2012 - Lecture 14 - Graph Algorithms (con't)
This is Lecture 14 of the CSE373 (Analysis of Algorithms) course taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 2012.
From playlist CSE373 - Analysis of Algorithms - 2012 SBU
Prim's Minimum Spanning Tree Algorithm | Graph Theory
Prim's Minimum Spanning Tree Algorithm Support me by purchasing the full graph theory course on Udemy which includes additional problems, exercises and quizzes not available on YouTube: https://www.udemy.com/course/graph-theory-algorithms Algorithms repository: https://github.com/william
From playlist Graph Theory Playlist
CSE 373 -- Lecture 14, Fall 2020
From playlist CSE 373 -- Fall 2020