Geometric graphs | Geometric algorithms | NP-hard problems | Trees (graph theory)
The rectilinear Steiner tree problem, minimum rectilinear Steiner tree problem (MRST), or rectilinear Steiner minimum tree problem (RSMT) is a variant of the geometric Steiner tree problem in the plane, in which the Euclidean distance is replaced with the rectilinear distance. The problem may be formally stated as follows: given n points in the plane, it is required to interconnect them all by a shortest network which consists only of vertical and horizontal line segments. It can be shown that such a network is a tree whose vertices are the input points plus some extra points (Steiner points). The problem arises in the physical design of electronic design automation. In VLSI circuits, wire routing is carried out by wires running only in vertical and horizontal directions, due to high computational complexity of the task. Therefore wire length is the sum of the lengths of vertical and horizontal segments, and the distance between two pins of a net is actually the rectilinear distance ("Manhattan distance") between the corresponding geometric points in the design plane. (Wikipedia).
Karol Węgrzycki: A Gap-ETH-Tight Approximation Scheme for Euclidean TSP
We revisit the classic task of finding the shortest tour of n points in d-dimensional Euclidean space, for any fixed constant d greater than 2. We determine the optimal dependence on ε in the running time of an algorithm that computes a (1 + ε)-approximate tour, under a plausible assumptio
From playlist Workshop: Approximation and Relaxation
This shows a 3d printed mobile produced using shapeways.com. This is joint work with Marco Mahler. This is available at http://shpws.me/nPha.
From playlist 3D printing
Using a set of points determine if the figure is a parallelogram using the midpoint formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Determining if a set of points makes a parallelogram or not
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Morphing symmetric binary branching tree
A symmetric binary tree is obtained by applying certain affine linear transformations recursively to the leaves starting with a trunk of unit length. This video shows a scale factor given by the golden ratio (well, roughly 0.618) and morphs between various angles of rotation. To build yo
From playlist Fractals
Determine if a set of points is a parallelogram using the distance formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Determine if a set of points makes up a rectangle using the distance formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Determining if a set of points is a rhombus, square or rectangle
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Jennifer Tour Chayes (Microsoft Research New England and Microsoft Research New York City) URL: https://www.icts.res.in/lecture/4/details/1644/ Description: Everywhere we turn these days, we find that networks can be used to describe relevant interactions.In the high tech world, we see th
From playlist Distinguished Lectures
Rainbow structures, Latin squares & graph decompositions - Benny Sudakov
Computer Science/Discrete Mathematics Seminar I Topic: Rainbow structures, Latin squares & graph decompositions Speaker: Benny Sudakov Affiliation: ETH Zürich Date: March 01, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Construct a minimum network using Torricelli's construction for a Steiner point in GeoGebra.
From playlist Discrete Math
How to determine if points are a rhombus, square or rectangle
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Discrete Math Test Review - Minimum Networks
This video shows the student how to solve a variety of problems related to minimum networks.
From playlist Discrete Math
Symmetric Binary Trees (visual construction)
In this video, we see how to change use two parameters (scale factor and angle of rotation) to create various symmetric binary trees. We show five different examples of such trees (up to level 13). Choose your own parameters and create your own! Check out these videos for related construc
From playlist Fractals
Jennifer Tour Chayes: Data scientists seeking personalized disease treatments
The study of networks by data scientists is leading to new business models that may someday result in innovative drug therapies keyed to individual patients, said Jennifer Tour Chayes, managing director and distinguished scientist at Microsoft Research. Research into the networks that regu
From playlist Women In Data Science Conference (WiDS)- 2015
Dana S Richards - Are You a Mathematician? - G4G14 April 2022
Martin Gardner is best known as a writer of recreational mathematics. It is often said he was not a mathematician; he said so himself. However he often contributed original results. These are found in math journals, his column and in the magic literature.
From playlist G4G14 Videos
This video provides a demonstration for constructing a Steiner Point in a network with three vertices. I use the Smart Notebook digital math tools which include a compass and ruler to guide students in the construction of a Steiner Point.
From playlist Discrete Math
Ramamoorthi Ravi: Designing Overlapping Networks for Publish Subscribe Systems
From the publish-subscribe systems of the early days of the Internet to the recent emergence of Web 3.0 and IoT (Internet of Things), new problems arise in the design of networks centered at producers and consumers of constantly evolving information. In a typical problem, each terminal is
From playlist HIM Lectures: Trimester Program "Combinatorial Optimization"
How to determine if a set of points is a rectangle, rhombus or square
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane