Combinatorial optimization | Optimization algorithms and methods
Branch and bound (BB, B&B, or BnB) is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic enumeration of candidate solutions by means of state space search: the set of candidate solutions is thought of as forming a rooted tree with the full set at the root. The algorithm explores branches of this tree, which represent subsets of the solution set. Before enumerating the candidate solutions of a branch, the branch is checked against upper and lower estimated bounds on the optimal solution, and is discarded if it cannot produce a better solution than the best one found so far by the algorithm. The algorithm depends on efficient estimation of the lower and upper bounds of regions/branches of the search space. If no bounds are available, the algorithm degenerates to an exhaustive search. The method was first proposed by Ailsa Land and Alison Doig whilst carrying out research at the London School of Economics sponsored by British Petroleum in 1960 for discrete programming, and has become the most commonly used tool for solving NP-hard optimization problems. The name "branch and bound" first occurred in the work of Little et al. on the traveling salesman problem. Branch and bound methods do not go deep like Depth-first search; the first direction is lateral movement in the tree similar to Breadth-first search (BFS). (Wikipedia).
In this video we review the basic components of a parabola
From playlist Parabolas
Parallel and Perpendicular Lines
Parallel and Perpendicular lines are easy to do - once you know how! Here's your quick intro to parallel and perpendicular lines. Have a great day! Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it
From playlist Algebra
What is the difference of a trapezoid and an isosceles trapezoid
👉 Learn how to solve problems with trapezoids. A trapezoid is a four-sided shape (quadrilateral) such that one pair of opposite sides are parallel. Some of the properties of trapezoids are: one pair of opposite sides are parallel, etc. A trapezoid is isosceles is one pair of opposite sides
From playlist Properties of Trapezoids
Rotation transmission between parallel shafts, one can move. The key factor is: 4 belt branches connecting to the green and blue pulleys must be parallel. It uses rope and flat belts, not V-belts. Inventor files of this video: http://www.mediafire.com/file/92mo39k7kqkgzde/BeltDrive8Inv.z
From playlist Mechanisms
An embodiment of "Sarrus linkage 1". Two planes of two planar slider-crank mechanisms are not necessary to be perpendicular to each other. It is enough that they are not parallel.
From playlist Mechanisms
Limit Points In this video, I define the notion of a limit point (also known as a subsequential limit) and give some examples of limit points. Limit points are closed: https://youtu.be/b1jYloJXDYY Check out my Sequences Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCuFxFs
From playlist Sequences
In this video we review the basic components of a parabola
From playlist Parabolas
In this video we review the basic components of a parabola
From playlist Parabolas
What are parallel lines and a transversal
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
Pseudorandom generators for unordered branching programs - Eshan Chattopadhyay
http://www.math.ias.edu/seminars/abstract?event=129025 More videos on http://video.ias.edu
From playlist Mathematics
Nexus Trimester - Paul Beame (University of Washington) - 3
Branching Programs 3/3 Paul Beame (University of Washington) February 26,2016 Abstract: Branching programs are clean and simple non-uniform models of computation that capture both time and space simultaneously. We present the best methods known for obtaining lower bounds on the size of (l
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
Nexus Trimester- Paul Beame (University of Washington) - 1
Branching Programs 2/3 Paul Beame (University of Washington) February 26,2016 Abstract: Branching programs are clean and simple non-uniform models of computation that capture both time and space simultaneously. We present the best methods known for obtaining lower bounds on the size of (l
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
Proving super-polynomial lower bounds for syntactic multilinear branching programs by Ramya C
Discussion Meeting Workshop on Algebraic Complexity Theory  ORGANIZERS Prahladh Harsha, Ramprasad Saptharishi and Srikanth Srinivasan DATE & TIME 25 March 2019 to 29 March 2019 VENUE Madhava Lecture Hall, ICTS Bangalore Algebraic complexity aims at understanding the computationa
From playlist Workshop on Algebraic Complexity Theory 2019
Laurent Charlin: "Exact Combinatorial Optimization with Graph Convolutional Neural Networks"
Deep Learning and Combinatorial Optimization 2021 "Exact Combinatorial Optimization with Graph Convolutional Neural Networks" Laurent Charlin - HEC Montréal Abstract: Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convol
From playlist Deep Learning and Combinatorial Optimization 2021
Nexus Trimester - Paul Beame (University of Washington) - 1
Branching Programs 1/3 Paul Beame (University of Washington) February 26,2016 Abstract: Branching programs are clean and simple non-uniform models of computation that capture both time and space simultaneously. We present the best methods known for obtaining lower bounds on the size of (l
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
Sandra Müller: Lower bounds for the perfect set property at weakly compact cardinals
By the Cantor-Bendixson theorem, subtrees of the binary tree on $\omega$ satisfy a dichotomy - either the tree has countably many branches or there is a perfect subtree (and in particular, the tree has continuum manybranches, regardless of the size of the continuum). We generalize this to
From playlist Logic and Foundations
Delayed column generation in large scale integer optimization problems - Professor Raphael Hauser
Mixed linear integer programming problems play an important role in many applications of decision mathematics, including data science. Algorithms typically solve such problems via a sequence of linear programming approximations and a divide-and-conquer approach (branch-and-bound, branch-an
From playlist Data science classes
Proving Parallel Lines with Angle Relationships
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal