Geometric algorithms | Computational geometry
The Euclidean shortest path problem is a problem in computational geometry: given a set of polyhedral obstacles in a Euclidean space, and two points, find the shortest path between the points that does not intersect any of the obstacles. In two dimensions, the problem can be solved in polynomial time in a model of computation allowing addition and comparisons of real numbers, despite theoretical difficulties involving the numerical precision needed to perform such calculations. These algorithms are based on two different principles, either performing a shortest path algorithm such as Dijkstra's algorithm on a visibility graph derived from the obstacles or (in an approach called the continuous Dijkstra method) propagating a wavefront from one of the points until it meets the other. In three (and higher) dimensions the problem is NP-hard in the general case, but there exist efficient approximation algorithms that run in polynomial time based on the idea of finding a suitable sample of points on the obstacle edges and performing a visibility graph calculation using these sample points. There are many results on computing shortest paths which stays on a polyhedral surface. Given two points s and t, say on the surfaceof a convex polyhedron, the problem is to compute a shortest path that never leaves the surface and connects s with t. This is a generalization of the problem from 2-dimension but it is much easier than the 3-dimensional problem. Also, there are variations of this problem, where the obstacles are weighted, i.e., one can go through an obstacle, but it incursan extra cost to go through an obstacle. The standard problem is the special case where the obstacles have infinite weight. This istermed as the in the literature. (Wikipedia).
Longest Simple Path - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Find the Shortest Path - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
The Shortest Way Home- An Unexpected Result
A story about how I stumbled on a very surprising result on my way home. Apparently math isn't entirely useless! Sorry about the sound :(
From playlist Some fun math videos about approximation
Find the Shortest Path - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Sometimes The Shortest Distance Between Two Points is NOT a Straight Line: GEODESICS by Parth G
What happens when the shortest distance between two points is NOT a straight line, and exactly what is a geodesic? Hey everyone, in this video we'll be looking at how the surface we happen to be studying impacts the definition of the "shortest" distance between two points on that surface.
From playlist Relativity by Parth G
Determining the Shortest Distance Between a Line and a Point
http://mathispower4u.wordpress.com/
From playlist Properties of Perpendicular Lines
Graph Data Structure 4. Dijkstra’s Shortest Path Algorithm
This is the fourth in a series of computer science videos about the graph data structure. This is an explanation of Dijkstra’s algorithm for finding the shortest path between one vertex in a graph and another. Indeed, this explains how Dijkstra’s shortest path algorithm generates a set o
From playlist Path Finding Algorithms
Longest Simple Path - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
The Shortest Distance Between A and B, with Two Reflections.
We present the solution to the shortest path problem between two given points with the constraint that the path needs to touch both x-axis and y-axis. A related problem is the Heron's shortest path problem. We give an visual animation of the problem and high level proof ideas. Both types
From playlist Geometry Problems for AMC Prep
Ernesto Estrada - Network bypasses sustain complexity - IPAM at UCLA
Recorded 31 August 2022. Ernesto Estrada of the University of the Balearic Islands (Illes Balears) presents "Network bypasses sustain complexity" at IPAM's Reconstructing Network Dynamics from Data: Applications to Neuroscience and Beyond. Abstract: Real-world networks are neither regular
From playlist 2022 Reconstructing Network Dynamics from Data: Applications to Neuroscience and Beyond
Advanced General Relativity: A Centennial Tribute to Amal Kumar Raychaudhuri (L5) by Sunil Mukhi
Seminar Lecture Series - Advanced General Relativity: A Centennial Tribute to Amal Kumar Raychaudhuri Speaker: Sunil Mukhi (IISER Pune) Date : Mon, 20 March 2023 to Fri, 21 April 2023 Venue: Online (Zoom & Youtube) ICTS is pleased to announce special lecture series by Prof. Sunil Mukh
From playlist Lecture Series- Advanced General Relativity: A Centennial Tribute to Amal Kumar Raychaudhuri -2023
Andreas E. Feldmann: A (1+ε)-embedding of low highway dimension graphs into bounded treewidth graphs
Andreas Emil Feldmann: A (1+ε)-embedding of low highway dimension graphs into bounded treewidth graphs Graphs with bounded highway dimension were introduced in [Abraham et al., SODA 2010] as a model of transportation networks. We show that any such graph can be embedded into a distributio
From playlist HIM Lectures 2015
Kaapi with Kuriosity: Tilings (ONLINE) by Mahuya Datta
Kaapi with Kuriosity Tilings (ONLINE) Speaker: Mahuya Datta (Indian Statistical Institute, Kolkata) When: 4:00 pm to 5:30 pm Sunday, 27 March 2022 Where: Zoom meeting and Livestream on ICTS YouTube channel Abstract: Tiling is a way of arranging plane shapes so that they completely co
From playlist Kaapi With Kuriosity (A Monthly Public Lecture Series)
New Methods in Finsler Geometry - 23 May 2018
http://www.crm.sns.it/event/415 Centro di Ricerca Matematica Ennio De Giorgi The workshop has limited funds to support lodging (and in very exceptional cases, travel) costs of some participants, with priority given to young researchers. When you register, you will have the possibility to
From playlist Centro di Ricerca Matematica Ennio De Giorgi
Tensor Calculus Lecture 15: Geodesic Curvature Preview
This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: http://bit.ly/MCTensors Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Te
From playlist Introduction to Tensor Calculus
Metric and manifold repair for missing data - Anna Gilbert
Virtual Workshop on Missing Data Challenges in Computation Statistics and Applications Topic: Metric and manifold repair for missing data Speaker: Anna Gilbert Date: September 11, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Did you ever wonder what is the shape of an object? Of the Earth? Of the galaxies? Well... get ready for the shape of something bigger! #SoMe1 #SummerOfMathExposition
From playlist Summer of Math Exposition Youtube Videos
Floyd-Warshall - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Tobias Mueller: Percolation on hyperbolic Poisson-Voronoi tessellations
I will discuss percolation on the Voronoi tessellation generated by a homogeneous Poisson point process on the hyperbolic plane. That is, we colour each cell of the hyperbolic Poisson-Voronoi tessellation black with probability p and white with probability 1 − p, independently of the colou
From playlist Workshop: High dimensional spatial random systems