Computational problems in graph theory | Combinatorial optimization | Hamiltonian paths and cycles | Travelling salesman problem | NP-complete problems | Graph algorithms | NP-hard problems
The travelling salesman problem (also called the travelling salesperson problem or TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research. The travelling purchaser problem and the vehicle routing problem are both generalizations of TSP. In the theory of computational complexity, the decision version of the TSP (where given a length L, the task is to decide whether the graph has a tour of at most L) belongs to the class of NP-complete problems. Thus, it is possible that the worst-case running time for any algorithm for the TSP increases superpolynomially (but no more than exponentially) with the number of cities. The problem was first formulated in 1930 and is one of the most intensively studied problems in optimization. It is used as a benchmark for many optimization methods. Even though the problem is computationally difficult, many heuristics and exact algorithms are known, so that some instances with tens of thousands of cities can be solved completely and even problems with millions of cities can be approximated within a small fraction of 1%. The TSP has several applications even in its purest formulation, such as planning, logistics, and the manufacture of microchips. Slightly modified, it appears as a sub-problem in many areas, such as DNA sequencing. In these applications, the concept city represents, for example, customers, soldering points, or DNA fragments, and the concept distance represents travelling times or cost, or a similarity measure between DNA fragments. The TSP also appears in astronomy, as astronomers observing many sources will want to minimize the time spent moving the telescope between the sources; in such problems, the TSP can be embedded inside an optimal control problem. In many applications, additional constraints such as limited resources or time windows may be imposed. (Wikipedia).
The Travelling Salesman (1 of 3: Understanding the Problem)
More resources available at www.misterwootube.com
From playlist Exploring Mathematics: Fractals
AQA Decision 1 8.01 The Travelling Salesperson Problem: An Introduction
I introduce the concept of the Travelling Salesperson problem and how we are going to go about attempting to solve it.
From playlist [OLD SPEC] TEACHING AQA DECISION 1 (D1)
MA 15: Traveling salesman problem brute force & sorted edges
This video is for my Spring 2020 section of MA 15, for the class meeting on Tuesday April 21. Fast forward music is from "Now Get Busy" by the Beastie Boys, licensed Creative Commons Noncommercial Sampling Plus.
From playlist Math 15 Spring 2020
From playlist M. Graph Theory
Travelling salesperson problem (Decision Maths 1)
Powered by https://www.numerise.com/ Travelling salesperson problem (Decision Maths 1). A video showing how to calculate an upper bound and lower bound as well as the nearest neighbour solution. Finally I finish off by showing how to use the tour improvement algorithm to attempt to find
From playlist Decision Maths 1 OCR Exam Board (A-Level tutorials)
AQA Decision 1 8.03 The Travelling Salesperson Problem: An example of a Hamiltonian Cycle / Tour
By inspection, I find a Hamiltonian cycle that may or may not be improved upon as a solution for the Travelling Salesperson Problem
From playlist [OLD SPEC] TEACHING AQA DECISION 1 (D1)
What's the difference between travel, journey, trip and voyage?
Are you confused about when to use the words travel, journey trip and voyage? In this video you'll find out with examples of usage. For more English language learning videos subscribe to LetThemTalkTV http://www.youtube.com/user/letthemtalkparis?sub_confirmation=1 Find out more about
From playlist The most common mistakes of English grammar and vocabulary
The Travelling Salesman (2 of 3: Nearest Neighbour & SFCs)
More resources available at www.misterwootube.com
From playlist Exploring Mathematics: Fractals
Coding Challenge #35.1: Traveling Salesperson
In Part 1 of this multi-part Coding Challenge, I introduce the classic computer science Traveling Salesperson problem ("traveling salesman" (sic) for search) and discuss the pitfalls with a brute force solution. đź’»Challenge Webpage: https://thecodingtrain.com/CodingChallenges/035.1-tsp.ht
From playlist Session 1 - Algorithms and Graphs - Intelligence and Learning
Traveling Salesman Problem | Dynamic Programming | Graph Theory
Solving the traveling salesman problem using dynamic programming Related Videos: TSP intro: https://www.youtube.com/watch?v=cY4HiiFHO1o TSP code video: https://www.youtube.com/watch?v=udEe7Cv3DqU Source code: https://github.com/williamfiset/algorithms#graph-theory Powerset backtracking
From playlist Graph Theory Playlist
Approximation Algs. - Lecture 19
All rights reserved for http://www.aduni.org/ Published under the Creative Commons Attribution-ShareAlike license http://creativecommons.org/licenses/by-sa/2.0/ Tutorials by Instructor: Shai Simonson. http://www.stonehill.edu/compsci/shai.htm Visit the forum at: http://www.coderisland.c
From playlist ArsDigita Algorithms by Shai Simonson
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
Travelling Salesman Problem source code | Dynamic Programming | Graph Theory
Source code for the traveling salesman problem with dynamic programming 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 Related videos:
From playlist Graph Theory Playlist
The Million Dollar Equations - with Tom Crawford
In the year 2000 it was announced that seven of the biggest unsolved problems in mathematics would each be given a $1million prize. Only one has been solved. Watch the Q&A: https://youtu.be/AFc7kGfLSIc Subscribe for regular science videos: http://bit.ly/RiSubscRibe The seven million dolla
From playlist Livestreams
R9. Approximation Algorithms: Traveling Salesman Problem
MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Amartya Shankha Biswas In this recitation, problems related to approximation algorithms are discussed, namely the traveling salesman problem. License: Creative Com
From playlist MIT 6.046J Design and Analysis of Algorithms, Spring 2015
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
NP Completeness III - More Reductions - Lecutre 17
All rights reserved for http://www.aduni.org/ Published under the Creative Commons Attribution-ShareAlike license http://creativecommons.org/licenses/by-sa/2.0/ Tutorials by Instructor: Shai Simonson. http://www.stonehill.edu/compsci/shai.htm Visit the forum at: http://www.coderisland.c
From playlist ArsDigita Algorithms by Shai Simonson